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1. Geometric analysis [2012]
 Li, Peter, 1952
 Cambridge ; New York : Cambridge University Press, 2012.
 Description
 Book — x, 406 pages ; 24 cm.
 Summary

 Introduction
 1. First and second variational formulas for area
 2. Volume comparison theorem
 3. BochnerWeitzenbock formulas
 4. Laplacian comparison theorem
 5. Poincare inequality and the first eigenvalue
 6. Gradient estimate and Harnack inequality
 7. Mean value inequality
 8. Reilly's formula and applications
 9. Isoperimetric inequalities and Sobolev inequalities
 10. The heat equation
 11. Properties and estimates of the heat kernel
 12. Gradient estimate and Harnack inequality for the heat equation
 13. Upper and lower bounds for the heat kernel
 14. Sobolev inequality, Poincare inequality and parabolic mean value inequality
 15. Uniqueness and maximum principle for the heat equation
 16. Large time behavior of the heat kernel
 17. Green's function
 18. Measured NeumannPoincare inequality and measured Sobolev inequality
 19. Parabolic Harnack inequality and regularity theory
 20. Parabolicity
 21. Harmonic functions and ends
 22. Manifolds with positive spectrum
 23. Manifolds with Ricci curvature bounded from below
 24. Manifolds with finite volume
 25. Stability of minimal hypersurfaces in a 3manifold
 26. Stability of minimal hypersurfaces in a higher dimensional manifold
 27. Linear growth harmonic functions
 28. Polynomial growth harmonic functions
 29. Lq harmonic functions
 30. Mean value constant, Liouville property, and minimal submanifolds
 31. Massive sets
 32. The structure of harmonic maps into a CartanHadamard manifold Appendix A. Computation of warped product metrics Appendix B. Polynomial growth harmonic functions on Euclidean space References Index.
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QA360 .L53 2012  Unknown 
2. Geometric realizations of curvature [2012]
 BrozosVázquez, Miguel.
 London, England : Imperial College Press, c2012.
 Description
 Book — ix, 252 p. ; 24 cm.
 Summary

 Introduction and Statement of Results Representation Theory Connections, Curvature, and Differential Geometry Affine Geometry Kahler and ParaKahler Geometry Affine Geometry Riemannian Geometry Complex and ParaComplex Geometry Hyper Complex Geometry and Other Questions.
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 www.worldscientific.com World Scientific
 EBSCO University Press
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QA360 .B76 2012  Unknown 
3. Discrete geometric analysis [2016]
 [Tokyo] : Mathematical Society of Japan, 2016.
 Description
 Book — xi, 157 pages : illustrations ; 25 cm.
 Summary

 Loop erased walks and uniform spanning trees / Martin T. Barlow
 Combinatorial rigidity: graphs and matroids in the theory of rigid frameworks / Tibor Jordán
 Analysis and geometry on groups / Andrzej Zuk.
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QA360 .D57 2016  Unknown 
4. Geometric analysis [2016]
 [Providence] : American Mathematical Society Institute for Advanced Study, [2016]
 Description
 Book — xvi, 438 pages : illustrations (some color) ; 27 cm.
 Summary

 * Heat diffusion in geometry by G. Huisken* Applications of Hamilton's compactness theorem for Ricci flow by P. Topping* The KahlerRicci flow on compact Kahler manifolds by B. Weinkove* Park City lectures on eigenfunctions by S. Zelditch* Critical metrics for Riemannian curvature functionals by J. A. Viaclovsky* Minmax theory and a proof of the Willmore conjecture by F. C. Marques and A. Neves* Weak immersions of surfaces with $L^2$bounded second fundamental form by T. Riviere* Introduction to minimal surface theory by B. White.
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QA360 .G455 2016  Unknown 
 Helgason, Sigurdur, 1927
 New York : Springer, c2011.
 Description
 Book — xiii, 301 p.
 Online

 dx.doi.org SpringerLink
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 TbilisiSalerno Workshop on Modeling in Mathematics (2nd : 2015 : Tbilisi, Georgia)
 [France] : Atlantis Press, 2017.
 Description
 Book — 1 online resource ( x, 185 pages) : illustrations (some color).
 Summary

 Introduction; Fractional
 Calculus
 Based FDTD Algorithm for Ultra
 Wideband Electromagnetic Pulse Propagation in Complex Layered Havriliak
 Negami Media;
 1 Introduction;
 2 Mathematical Formulation;
 3 Numerical Results;
 4 Conclusion; References; Spherical Harmonic Solution of the Robin Problem for the Laplace Equation in Supershaped Shells;
 1 Introduction;
 2 The Laplacian in Stretched Spherical Coordinates;
 3 The Robin Problem for the Laplace Equation;
 4 Numerical Procedure; 4.1 Example 1; 4.2 Example 2;
 5 Conclusion; References
 Evolution Equations Involving Matrices Raised to NonInteger Exponents1 Introduction;
 2 Fractional Matrix Exponentiation;
 3 A Physical Application;
 4 Final Comments; References; Hermite Calculus;
 1 Introduction;
 2 The Umbral Method and Generalized Hermite Polynomials;
 3 Final Comments; References; Modal Epistemic Łukasiewicz Logic with Constant and Its Application in Immune System;
 1 Introduction;
 2 Multimodal Epistemic 3Valued Łukasiewicz Logics EŁ3c(n); 2.1 3Valued Descriptive Kripke Models; 2.2 Axiomatization;
 3 On the Cells of Immune System
 4 Description of Immune System by Descriptive Kripke Frames4.1 The Epistemic Aspects of Immune System;
 5 Conclusion and Perspectives; References; Potential Fields of Self Intersecting Gielis Curves for Modeling and Generalized Blending Techniques;
 1 Introduction;
 2 From Gielis Curves to Radial Distance Fields;
 3 RFunctions; 3.1 Systems of RFunctions and Some Properties; 3.2 From the Geometric Interpretations of Binary RFunctions to Generalized Blending;
 4 Potential Field Equation for Rational Gielis Curves;
 5 Conclusions and Future Work; References
 A Biogeometrical Model for Corolla Fusion in Asclepiad Flowers1 Introduction;
 2 Gielis Flower Domains and Associated Laplacian;
 3 Leaf Shapes and Phyllotaxy;
 4 Corolla Shapes in Asclepiad Flowers;
 5 A ThreeElement System for Fusion in Corolla;
 6 Fourier
 Bessel Solution for the Helmholtz Equation;
 7 Leaves and Corollas;
 8 Fourier Projection Method as a General Method for BVP;
 9 Fast Forward Evolution: Combining Stochastic and Deterministic Techniques;
 10 Conclusion; References; A Note About Generalized Forms of the Gielis Formula;
 1 Introduction;
 2 Notable Properties of the Gielis Formula
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7. Geometric and spectral analysis [2014]
 Providence, Rhode Island : American Mathematical Society ; Montreal, Quebec, Canada : Centre de Recherches Mathematiques, [2014]
 Description
 Book — x, 366 pages : illustrations ; 26 cm.
 Summary

 A new proof of a BismutZhang formula for some class of representations by M. Braverman and B. Vertman Tunneling, the Quillen metric and analytic torsion for high powers of a holomorphic line bundle by R. J. Berman Simple spectrum and Rayleigh quotients by V. Guillemin, E. Legendre, and R. SenaDias Smooth and singular KahlerEinstein metrics by Y. A. Rubinstein Complex $b$manifolds by G. A. Mendoza Iterative structures on singular manifolds by B.W. Schulze The fundamental gap and onedimensional collapse by Z. Lu and J. Rowlett The logarithmic singularities of the Green functions of the conformal powers of the Laplacian by R. Ponge A symbolic calculus for Fourier integral operators by Y. Safarov Strichartz estimates on exterior polygonal domains by D. Baskin, J. L. Marzuola, and J. Wunsch Probabilistic Sobolev embeddings, applications to eigenfunctions estimates by N. Burq and G. Lebeau Random smooth functions on compact Riemannian manifolds by L. I. Nicolaescu On the exponential decay of Laplacian eigenfunctions in planar domains with branches by B. T. Nguyen, D. S. Grebenkov, and A. L. Delytsin Bounds on the principal frequency of the $p$Laplacian by G. Poliquin.
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QC20.7 .S64 G46 2014  Unknown 
8. IsoGeometric analysis : a new paradigm in the numerical approximation of PDEs : Cetraro, Italy 2012 [2016]
 [Cham] Switzerland : Springer ; [Cetraro] : Fondazione CIME Roberto Conti, [2016]
 Description
 Book — ix, 193 pages : color illustrations ; 23 cm.
 Summary

 Preface. Standard and NonStandard CAGD Tool for Isogeometric Analysis: a Tutorial. Models for Isogeometric Analysis from CAD. An Introduction to the Numerical Analysis of Isogeometric Methods. Isogeometric Compatible Discretizations for Viscous Incompressible Flow.
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Shelved by Series title V.2161  Unknown 
 AriasCastro, Ery.
 Stanford, Calif. : Department of Statistics, Stanford University, 2003.
 Description
 Book — 21 leaves. ; 28 cm.
SAL3 (offcampus storage)
SAL3 (offcampus storage)  Status 

For use in Special Collections Reading Room  Request onsite access 
260290  Inlibrary use 
Stacks  Request 
260290  Available 
 Providence, R.I. : American Mathematical Society, c2011.
 Description
 Book — vii, 213 p. : ill. ; 26 cm.
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QC20.7 .S64 S644 2011  Unknown 
 Berlin : SpringerVerlag, c2009.
 Description
 Book — xiii, 278 p. : ill. ; 24 cm.
 Summary

 PDEs in Conformal Geometry. Heat kernels in subRiemannian settings. Concentration of solutions for some singularly perturbed Neumann problems. On some elliptic problems in the study of selfdualChernSimons vortices. The kHessian equation. Minimal Surfaces in CR Geometry.
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Shelved by Series title V.1977  Unknown 
Online 12. Adaptive multiscale detection of filamentary structures embedded in a background of uniform random points [2003]
 AriasCastro, Ery.
 Stanford, Calif. : Department of Statistics, Stanford University, 2003.
 Description
 Book — 1 online resource (21 pages)
 Also online at
 Papers. Selections
 Ding, Weiyue.
 Singapore : World Scientific Publishing Co. Pte Ltd., ©2018.
 Description
 Software/Multimedia — 1 online resource (633 p).
 Summary

"This collection covers all papers and partial talks given by Prof Weiyue Ding, who was a member of the Chinese Academy of Sciences. Prof Weiyue Ding devoted his academic career to the research in the field of ordinary differential equations and geometric analysis, e.g. Poincaré–Birkhoff fixed point theorems, blowup analysis for heat flow of harmonic maps." Provided by publisher.
 AlonsoGutierrez, David, author.
 Cham : Springer, [2015]
 Description
 Book — x, 148 pages ; 24 cm.
 Summary

 The Conjectures. Main Examples. Relating the Conjectures. Appendix. Index.
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Science Library (Li and Ma)
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Serials  
Shelved by Series title V.2131  Unknown 
Online 15. Nearoptimal detection of geometric objects by fast multiscale methods [2003]
 AriasCastro, Ery author.
 Stanford, Calif. : Department of Statistics, Stanford University, August 2003.
 Description
 Book — 1 online resource (56 pages).
 Also online at

16. Geometric and topological inference [2018]
 Boissonnat, J.D. (JeanDaniel), 1953 author.
 Cambridge : Cambridge University Press, 2018.
 Description
 Book — 1 online resource (xii, 233 pages0 : digital, PDF file(s).
 Summary

 Part I. Topological Preliminaries:
 1. Topological spaces
 2. Simplicial complexes Part II. Delaunay Complexes:
 3. Convex polytopes
 4. Delaunay complexes
 5. Good triangulations
 6. Delaunay filtrations Part III. Reconstruction of Smooth Submanifolds:
 7. Triangulation of submanifolds
 8. Reconstruction of submanifolds Part IV. DistanceBased Inference:
 9. Stability of distance functions
 10. Distance to probability measures
 11. Homology inference.
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17. Fractals in probability and analysis [2017]
 Bishop, Christopher J., author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2017.
 Description
 Book — ix, 402 pages : illustrations ; 24 cm.
 Summary

 1. Minkowski and Hausdorff dimensions
 2. Selfsimilarity and packing dimension
 3. Frostman's theory and capacity
 4. Selfaffine sets
 5. Graphs of continuous functions
 6. Brownian motion, part I
 7. Brownian motion, part II
 8. Random walks, Markov chains and capacity
 9. BesicovitchKakeya sets
 10. The traveling salesman theorem Appendix A. Banach's fixedpoint theorem Appendix B. Frostman's lemma for analytic sets Appendix C. Hints and solutions to selected exercises References Index.
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QA614.86 .B57 2017  Unknown 
18. Modelling and analysis of compositional data [2015]
 PawlowskyGlahn, Vera.
 Chichester, West Sussex : Wiley, 2015.
 Description
 Book — 1 online resource.
 Conde, Diogo Queiros, author.
 Amsterdam : Elsevier, 2018.
 Description
 Book — 1 online resource (1 volume) : illustrations (some color)
 Summary

 1. The Thermal Worm Model to Represent EntropyExergy Duality
 2. Black Hole Entropy and the Thermal Worm Model
 3. The Entropic Skins of BlackBody Radiation:a Geometrical Theory of Radiation
 4. Nonextensive Thermodynamics, Fractal Geometryand Scaleentropy
 5. Finite Physical Dimensions Thermodynamics
 6. A ScaleDependent Fractal and Intermittent Structure to Describe Chemical Potential and Matter Diffusion.
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 Singapore : World Scientific Publishing Co. Pte Ltd, c2016.
 Description
 Book — 1 online resource (221 p.) : ill.
 Summary

"This volume contains three expanded lecture notes from the program Scalar Curvature in Manifold Topology and Conformal Geometry that was held at the Institute for Mathematical Sciences from 1 November to 31 December 2014. The first chapter surveys the recent developments on the fourthorder equations with negative exponent from geometric points of view such as positive mass theorem and uniqueness results. The next chapter deals with the recent important progress on several conjectures such as the existence of nonflat smooth hypersurfaces and Serrin's overdetermined problem. And the final chapter induces a new technique to handle the equation with critical index and the sign change coefficient as well as the negative index term. These topics will be of interest to those studying conformal geometry and geometric partial differential equations."Provided by publisher.
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