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 Agler, Jim author.
 Providence, RI : American Mathematical Society, [2019]
 Description
 Book — vii, 108 pages ; 25 cm.
 Summary

 Introduction An overview Extremal problems in the symmetrized bidisc $G$ Complex geodesics in $G$ The retracts of $G$ and the bidisc $\mathbb {D}^2$ Purely unbalanced and exceptional datums in $G$ A geometric classification of geodesics in $G$ Balanced geodesics in $G$ Geodesics and sets $V$ with the normpreserving extension property in $G$ Anomalous sets $\mathcal {R}\cup \mathcal {D}$ with the normpreserving extension property in $G$ $V$ and a circular region $R$ in the plane Proof of the main theorem Sets in $\mathbb {D}^2$ with the symmetric extension property Applications to the theory of spectral sets Anomalous sets with the normpreserving extension property in some other domains Appendix A. Some useful facts about the symmetrized bidisc Appendix B. Types of geodesic: a crib and some cartoons Bibliography Index.
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Shelved by Series title NO.1242  Unknown 
 Providence, Rhode Island : American Mathematical Society ; [Stony Brook, New York] : Simons Center for Geometry and Physics, [2019]
 Description
 Book — xv, 298 pages : illustrations ; 27 cm.
 Summary

 Introduction / by John W. Morgan
 Notes on Kuranishi atlases / by Dusa McDuff
 GromovWitten theory via Kuranishi structures /rby Mohammad F. Tehrani and Kenji Fukaya
 Kuranishi spaces as a 2category / by Dominic Joyce.
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QA3 .A4 V.237  Unknown 
3. Curvature : a variational approach [2018]
 Agrachev, Andrei A., author.
 Providence, RI : American Mathematical Society, [2018]
 Description
 Book — v, 142 pages : illustrations ; 26 cm.
 Summary

 Chapter 1. Introduction
 Part 1. Statement of the results. Chapter 2. General setting
 Chapter 3. Flag and growth vector of an admissible curve
 Chapter 4. Geodesic cost and its asymptotics
 Chapter 5. SubRiemannian geometry
 Part 2. Technical tools and proofs. Chapter 6. Jacobi curves
 Chapter 7. Asymptotics of the Jacobi curve: Equiregular case
 Chapter 8. SubLaplacian and Jacobi curves
 Part 3. Appendix. Appendix A. Smoothness of value function (Theorem 2.19)
 Appendix B. Convergence of approximating Hamiltonian systems (Proposition 5.15)
 Appendix C. Invariance of geodesic growth vector by dilations (Lemma 5.20)
 Appendix D. Regularity of C(t,s) for the Heisenberg group (Proposition 5.51)
 Appendix E. Basics on curves in Grassmannians (Lemma 3.5 and 6.5)
 Appendix F. Normal conditions for the canonical frame
 Appendix G. Coordinate representation of flat, rank 1 Jacobi curves (Proposition 7.7)
 Appendix H. A binomial identity (Lemma 7.8)
 Appendix I. A geometrical interpretation of ct.
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Shelved by Series title NO.1225  Unknown 
 Honda, Shouhei, author.
 Providence, RI : American Mathematical Society, [2018]
 Description
 Book — v, 92 pages ; 26 cm.
 Summary

 Introduction Preliminaries $L^p$convergence revisited Poisson's equations Schrodinger operators and generalized Yamabe constants Rellich type compactness for tensor fields Differential forms Bibliography.
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Shelved by Series title NO.1211  Unknown 
 Cham, Switzerland : Springer Inernational Publishing, [2018]
 Description
 Book — vii, 125 pages : illustrations (some colored) ; 24 cm.
 Summary

 Complex differential equations and geometric structures on curves / Adolfo Guillot
 Blowup, homotopy and existence for periodic solutions of the planar threebody problem / Richard Montgomery
 A quick view of Lagrangian Floer homology / Andrés Pedroza.
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Shelved by Series title V.2204  Unknown 
6. Lie groups, geometry, and representation theory : a tribute to the life and work of Bertram Kostant [2018]
 Cham, Switzerland : Birkhäuser, [2018]
 Description
 Book — xii, 540 pages : illustrations ; 24 cm.
 Summary

 Anthony Joseph, A Tribute to Bertram Kostant. Anton Alekseev, Arkady Berenstein, Benjamin Hoffman, Yanpeng Li, Poisson Structures and Potentials. Tomoyuki Arakawa, Kazuya Kawasetsu, Quasilisse Vertex Algebras and Modular Linear Differential Equations. Roman Bezrukavnikov, Ivan Losev, On Dimension Growth of Modular Irreducible Representations of Semisimple Lie Algebras. Alexander Braverman, David Kazhdan, Remarks on the Asymptotic Hecke Algebra. Alexei Davydov, Pavel Etingof, Dmitri Nikshych, Autoequivalences of Tensor Categories Attached to Quantum Groups at Roots of 1. Victor Ginzburg, NilHecke Algebras and Whittaker $\mathscr{D}$Modules. V. Guillemin, A. Uribe, Z. Wang, Spectral Properties of Semiclassical Toeplitz Operators. Anthony Joseph, Dual Kashiwara Functions for the $B(\infty)$ Crystal. Victor G. Kac, Minoru Wakimoto, On Characters of Irreducible Highest Weight Modules of Negative Integer Level over Affine Lie Algebras. Thomas Lam, Alexander Postnikov, Alcoved Polytopes II. Ivan Losev, Representation Theory of Quantized Gieseker Varieties, I. JiangHua Lu, Yipeng Mi, Generalized Bruhat Cells and Completeness of Hamiltonian Flows of KoganZelevinsky Integrable Systems. G. Lusztig, On the Definition of Almost Characters. Eckhard Meinrenken, Verlinde Formulas for Nonsimply Connected Groups. PaulEmile Paradan, Michele Vergne, Equivariant Index of Twisted Dirac Operations and Semiclassical Limits. Vladimir L. Popov, Modality of Representations and Packets for $\theta$Groups. N. Ressayre, Distributions on Homogeneous Spaces and Applications. JeanPierre Serre, On the mod p reduction of orthogonal representations.
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QA387 .L535 2018  Unknown 
 Steeb, W.H., author.
 Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2018]
 Description
 Book — xi, 284 pages ; 24 cm
 Summary

A collection of problems and solutions in differential geometry, with applications.
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QA641 .S65 2018  Unknown 
8. Synthetic differential topology [2018]
 Bunge, M. (Marta), author.
 Cambridge : Cambridge University Press, 2018.
 Description
 Book — 223 pages ; 23 cm.
 Summary

 Introduction Part I. Toposes and Differential Geometry:
 1. Topos theory
 2. Synthetic differential geometry Part II. Topics in SDG:
 3. The AmbrosePalaisSinger theorem in SDG
 4. Calculus of variations in SDG Part III. Toposes and Differential Topology:
 5. Local concepts in SDG
 6. Synthetic differential topology Part IV. Topics in SDT:
 7. Stable mappings and Mather's theorem in SDT
 8. Morse theory in SDT Part V. SDT and Differential Topology:
 9. Welladapted models of SDT
 10. An application to unfoldings Part VI. A WellAdapted Model of SDT:
 11. The Dubuc topos G
 12. G as a model of SDT References Index.
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QA613.6 .B86 2018  Unknown 
9. Willmore energy and Willmore conjecture [2018]
 Boca Raton, FL : CRC Press, [2018]
 Description
 Book — xiii, 141 pages ; 24 cm.
 Summary

 Willmore Energy: Brief Introduction and Survey. Transformations of Generalized Harmonic bundles and Constrained Willmore Surfaces. Analytical Representations of Willmore and Generalized Willmore Surfaces. Construction of Willmore TwoSpheres Via Harmonic Maps Into SO+(1n + 3)=(SO+(1 1) SO(n + 2)). Towards a Constrained Willmore Conjecture.
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QA643 .W55 2018  Unknown 
 Wu, Hongxi, 1940 author.
 2017 edition.  Beijing : Higher Education Press, [2017]
 Description
 Book — xiii, 213 pages : portrait ; 25 cm.
 Summary

 Coordinates and frames normal at a point
 The Weitzenböck formulas
 Some results in the compact case
 Some results in the noncompact case
 Harmonic spinor fields
 Harmonic mapping
 Appendix: Vector fields and Ricci curvature by S. Bochner
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QA649 .W84 2017  Unknown 
11. Differential geometry & integral geometry : selected papers & lectures of ShiingShen Chern [2017]
 Chern, ShiingShen, 19112004.
 Somerville, Mass. : International Press ; Bejing : Higher Education Press, [2017]
 Description
 Book — xi, 246 pages : illustrations ; 26 cm.
 Summary

 Part I. What is geometry and differential geometry: What is geometry?
 Differential geometry : it past and its future
 Part II. Lectures on integral geometry
 Part III. Differentiable manifolds: Multilinear algebra
 Differentiable manifolds
 Exterior differential forms
 Affine connections
 Riemannian manifolds
 Part IV. Lecture notes on differentiable geometry: Review of surface theory
 Minimal surfaces
 Pseudospherical surface.
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QA641 .C445 2017  Unknown 
 Tu, Loring W., author.
 Cham, Switzerland : Springer, [2017]
 Description
 Book — xvi, 346 pages : illustrations (some color), portraits (some color) ; 24 cm.
 Summary

 Preface
 Curvature and vector fields
 Riemannian manifolds
 Inner products on a vector space
 Representations of inner products by symmetric matrices
 Riemannian metrics
 Existence of a riemannian metric
 Problems
 Curves
 Regular curves
 Arc length parametrization
 Signed curvature of a plane curve
 Orientation and curvature
 Problems
 Surfaces in space
 Principal, mean, and gaussian curvatures
 Gauss's theorema egregium
 The gaussbonnet theorem
 Problems
 Directional derivatives in euclidean space
 Directional derivatives in euclidean space
 Other properties of the directional derivative
 Vector fields along a curve
 Vector fields along a submanifold
 Directional derivatives on a submanifold of R...
 Problems
 The shape operator
 Normal vector fields
 The shape operator
 Curvature and the shape operator
 The first and second fundamental forms
 The catenoid and the helicoid
 Problems
 Affine connections
 Affine connections
 Torsion and curvature
 The riemannian connection
 Orthogonal projection on a surface in R³
 The riemannian connection on a surface in R³
 Problems
 Vector bundles
 Definition of a vector bundle
 The vector space of sections
 Extending a local section to a global section
 Local operators
 Restriction of a local operator to an open subset
 Frames
 ...Linearity and bundle maps
 Multilinear maps over smooth functions
 Problems
 Gauss's theorema egregium
 The gauss and codazzimainardi equations
 A proof of the theorema egregium
 The gaussian curvature in terms of an arbitrary basis
 Problems
 Generalizations to hypersurfaces in R...
 The shape operator of a hypersurface
 The riemannian connection of a hypersurface
 The second fundamental form
 The gauss curvature and codazzimainardi equations
 Curvature and differential forms
 Connections on a vector bundle
 Connections on a vector bundle
 Existence of a connection on a vector bundle
 Curvature of a connection on a vector bundle
 Riemannian bundles
 Metric connections
 Restricting a connection to an open subset
 Connections at a point
 Problems
 Connection, curvature, and torsion forms
 Connection and curvature forms
 Connections on a framed open set
 The gramschmidt process
 Metric connection relative to an orthonormal frame
 Connections on the tangent bundle
 Problems
 The theorema egregium using forms
 The gauss curvature equation
 The theorema egregium
 Skewsymmetries of the curvature tensor
 Sectional curvature
 Poincaré halfplane
 Problems
 Geodesies
 More on affine connections
 Covariant differentiation along a curve
 Connectionpreserving diffeomorphisms
 Christoffel symbols
 Problems
 Geodesies
 The definition of a geodesic
 Reparametrization of a geodesic
 Existence of geodesies
 Geodesies in the poincaré halfplane
 Parallel translation
 Existence of parallel translation along a curve
 Parallel translation on a riemannian manifold
 Problems
 Exponential maps
 The exponential map of a connection
 The differential of the exponential map
 Normal coordinates
 Leftinvariant vector fields on a lie group
 Exponential map for a lie group
 Naturality of the exponential map for a lie group
 Adjoint representation
 Associativity of a biinvariant metric on a lie group
 Problems
 Addendum : the exponential map as a natural transformation
 Distance and volume
 Distance in a riemannian manifold
 Geodesic completeness
 Dual 1forms under a change of frame
 Volume form
 The volume form in local coordinates
 Problems
 The gaussbonnet theorem
 Geodesic curvature
 The angle function along a curve
 Signed geodesic curvature on an oriented surface
 Gaussbonnet formula for a polygon
 Triangles on a riemannian 2manifold
 Gaussbonnet theorem for a surface
 Gaussbonnet theorem for a hypersurface in R²...
 Problems
 Tools from algebra and topology
 The tensor product and the dual module
 Construction of the tensor product
 Universal mapping property for bilinear maps
 Characterization of the tensor product
 A basis for the tensor product
 The dual module
 Identities for the tensor product
 Functoriality of the tensor product
 Generalization to multilinear maps
 Associativity of the tensor product
 The tensor algebra
 Problems
 The exterior power
 The exterior algebra
 Properties of the wedge product
 Universal mapping property for alternating klinear maps
 A basis for ... V
 Nondegenerate pairings
 A nondegenerate pairing of .... with ... V
 A formula for the wedge product
 Problems
 Operations on vector bundles
 Vector subbundles
 Subbundle criterion
 Quotient bundles
 The pullback bundle
 Examples of the pullback bundle
 The direct sum of vector bundles
 Other operations on vector bundles
 Problems
 Vectorvalued forms
 Vectorvalued forms as sections of a vector bundle
 Products of vectorvalued forms
 Directional derivative of a vectorvalued function
 Exterior derivative of a vectorvalued form
 Differential forms with values in a lie algebra
 Pullback of vectorvalued forms
 Forms with values in a vector bundle
 Tensor fields on a manifold
 The tensor criterion
 Remark on signs concerning vectorvalued forms
 Problems
 Vector bundles and characteristic classes
 Connections and curvature again
 Connection and curvature matrices under a change of frame
 Bianchi identities
 The first bianchi identity in vector form
 Symmetry properties of the curvature tensor
 Covariant derivative of tensor fields
 The second bianchi identity in vector form
 Ricci curvature
 Scalar curvature
 Defining a connection using connection matrices
 Induced connection on a pullback bundle
 Problems
 Characteristic classes
 Invariant polynomials on g...(r, R)
 The chernweil homomorphism
 Characteristic forms are closed
 Differential forms depending on a real parameter
 Independence of characteristic classes of a connection
 Functorial definition of a characteristic class
 Naturality
 Problems
 Pontrjagin classes
 Vanishing of characteristic classes
 Pontrjagin classes
 The whitney product formula
 The euler class and chern classes
 Orientation on a vector bundle
 Characteristic classes of an oriented vector bundle
 The pfaffian of a skewsymmetric matrix
 The euler class
 Generalized gaussbonnet theorem
 Hermitian metrics
 Connections and curvature on a complex vector bundle
 Chern classes
 Problems
 Some applications of characteristic classes
 The generalized gaussbonnet theorem
 Characteristic numbers
 The cobordism problem
 The embedding problem
 The hirzebruch signature formula
 The riemannroch problem
 Principal bundles and characteristic classes
 Principal bundles
 Principal bundles
 The frame bundle of a vector bundle
 Fundamental vector fields of a right action
 Integral curves of a fundamental vector field
 Vertical subbundle of the tangent bundle TP
 Horizontal distributions on a principal bundle
 Problems
 Connections on a principal bundle
 Connections on a principal bundle
 Vertical and horizontal components of a tangent vector
 The horizontal distribution of an ehresmann connection
 Horizontal lift of a vector field to a principal bundle
 Lie bracket of a fundamental vector field
 Problems
 Horizontal distributions on a frame bundle
 Parallel translation in a vector bundle
 Horizontal vectors on a frame bundle
 Horizontal lift of a vector field to a frame bundle
 Pullback of a connection on a frame bundle under a section
 Curvature on a principal bundle
 Curvature form on a principal bundle
 Properties of the curvature form
 Problems
 Covariant derivative on a principal bundle
 The associated bundle
 The fiber of the associated bundle
 Tensorial forms on a principal bundle
 Covariant derivative
 A formula for the covariant derivative of a tensorial form
 Problems
 Characteristic classes of principal bundles
 Invariant polynomials on a lie algebra
 The chernweil homomorphism
 Problems
 Appendix
 Manifolds
 Manifolds and smooth maps
 Tangent vectors
 Vector fields
 Differential forms
 Exterior differentiation on a manifold
 Exterior differentiation on R³
 Pullback of differential forms
 Problems
 Invariant polynomials
 Polynomials versus polynomial functions
 Polynomial identities
 Invariant polynomials on g...(r, F)
 Invariant complex polynomials
 Lpolynormals, todd polynomials, and the chern character
 Invariant real polynomials
 Newton's identities
 Problems
 Hints and solutions to selected endofsection problems
 List of notations
 References
 Index.
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QA641 .T76 2017  Unknown 
13. Differential geometry of curves and surfaces [2017]
 Kyokusen to kyokumen. English
 曲線と曲面. English
 Umehara, Masaaki, author.
 Kaiteiban = Revised edition [1st English edition].  Singapore ; New Jersey : World Scientific, [2017]
 Description
 Book — xii, 312 pages : illustrations ; 23 cm
 Summary

This engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a universitylevel course, without the need for referencing other texts, as it is completely selfcontained. More advanced material in the second half of the book, including appendices, also serves more experienced students well.Furthermore, this text is also suitable for a seminar for graduate students, and for selfstudy. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates.Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities.In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.
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QA641 .U4413 2017  Unknown 
 Lê, Nam Q., author.
 Cham, Switzerland : Springer, [2017]
 Description
 Book — vii, 228 pages : illustration ; 24 cm.
 Summary

 Part I. The second boundary value problem of the prescribed affine mean curvature equation and related linearized MongeAmpère equation / Nam Q. Le
 Part II. Dynamical properties of HamiltonJacobi equations via the nonlinear adjoint method : large time behavior and discounted approximation / Hiroyoshi Mitake and Hung V. Tran.
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Shelved by Series title V.2183  Unknown 
 Buium, Alexandru, 1955 author.
 Providence, Rhode Island : American Mathematical Society, [2017]
 Description
 Book — x, 344 pages ; 27 cm.
 Summary

 Algebraic backgroundClassical differential geometry revisitedArithmetic differential geometry: GeneralitiesArithmetic differential geometry: The case of $GL_n$Curvature and Galois groups of Ehresmann connectionsCurvature of Chern connectionsCurvature of LeviCivita connectionsCurvature of Lax connectionsOpen problemsBibliographyIndex.
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QA3 .A4 V.222  Unknown 
 Clelland, Jeanne N., 1970 author.
 Providence, Rhode Island : American Mathematical Society, [2017]
 Description
 Book — xvi, 414 pages : illustrations ; 26 cm.
 Summary

 * Background material: Assorted notions from differential geometry* Differential forms* Curves and surfaces in homogeneous spaces via the method of moving frames: Homogeneous spaces* Curves and surfaces in Euclidean space* Curves and surfaces in Minkowski space* Curves and surfaces in equiaffine space* Curves and surfaces in projective space* Applications of moving frames: Minimal surfaces in $\mathbb{E}^3$ and $\mathbb{A}^3$* Pseudospherical surfaces in Backlund's theorem* Two classical theorems* Beyond the flat case: Moving frames on Riemannian manifolds: Curves and surfaces in elliptic and hyperbolic spaces* The nonhomogeneous case: Moving frames on Riemannian manifolds* Bibliography* Index.
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QA433 .C564 2017  Unknown 
 Providence, Rhode Island : American Mathematical Society ; Montréal, Québec, Canada : Centre de Recherches Mathématiques, [2017]
 Description
 Book — ix, 284 pages ; 26 cm.
 Summary

 B. Colbois, The spectrum of the Laplacian: A geometric approach G. Berkolaiko, An elementary introduction to quantum graphs D. Bucur and P. Freitas, A free boundary approach to the FaberKrahn inequality P. Berard and B. Helffer, Some nodal properties of the quantum harmonic oscillator and other Schrodinger operators in $\mathbb{R}^2$ J. Bosch and C. Greif, Numerical solution of linear eigenvalue problems G. Kanschat, Finite element methods for variational eigenvalue problems A. Strohmaier, Computation of eigenvalues, spectral zeta functions and zetadeterminants on hyperbolic surfaces D. Grieser, Scales, blowup and quasimode constructions C. Guillarmou, Scattering for the geodesic flow on surfaces with boundary.
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QA611.28 .G46 2017  Unknown 
 Damon, James, 1945 author.
 Providence, Rhode Island : American Mathematical Society, [2017]
 Description
 Book — x, 163 pages : illustrations ; 26 cm.
 Summary

 Introduction
 Part 1. Medial/Skeletal Linking Structures: Multiregion configurations in $\mathbb{R}^{n+1}$Skeletal linking structures for multiregion configurations in ${\mathbb R}^{n+1}$Blum medial linking structure for a generic multiregion configurationRetracting the full Blum medial structure to a skeletal linking structure
 Part 2. Positional Geometry of Linking Structures: Questions involving positional geometry of a multiregion configurationShape operators and radial flow for a skeletal structureLinking flow and curvature conditionsProperties of regions defined using the linking flowGlobal geometry via medial and skeletal linking integralsPositional geometric properties of multiregion configurations
 Part 3. Generic Properties of Linking Structures via Transversality Theorems: Multidistance and heightdistance functions and partial multijet spacesGeneric Blum linking properties via transversality theoremsGeneric properties of Blum linking structuresConcluding generic properties of Blum linking structures
 Part 4. Proofs and Calculations for the Transversality Theorems: Reductions of the proofs of the transversality theoremsFamilies of perturbations and their infinitesimal propertiesCompleting the proofs of the transversality theoremsAppendix A. List of frequently used notationBibliography.
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Shelved by Series title NO.1193  Unknown 
 Figalli, Alessio, 1984 author.
 Zürich : European Mathematical Society, [2017]
 Description
 Book — x, 200 pages : illustrations ; 24 cm.
 Summary

"The MongeAmpère equation is one of the most important partial differential equations, appearing in many problems in analysis and geometry. This monograph is a comprehensive introduction to the existence and regularity theory of the MongeAmpère equation and some selected applications; the main goal is to provide the reader with a wealth of results and techniques he or she can draw from to understand current research related to this beautiful equation. The presentation is essentially selfcontained, with an appendix wherein one can find precise statements of all the results used from different areas (linear algebra, convex geometry, measure theory, nonlinear analysis, and PDEs). This book is intended for graduate students and researchers interested in nonlinear PDEs: explanatory figures, detailed proofs, and heuristic arguments make this book suitable for selfstudy and also as a reference."  Back cover.
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QA377 .F54 2017  Unknown 
 Gigli, Nicola, author.
 Providence, RI : American Mathematical Society, [2018]
 Description
 Book — v, 161 pages : illustrations ; 26 cm.
 Summary

 IntroductionThe machinery of $L^p(\mathfrak{m})$normed modulesFirst order differential structure of general metric measure spacesSecond order differential structure of $\mathsf{RCD}(K, \infty)$ spacesBibliography.
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Shelved by Series title NO.1196  Unknown 