Sets of finite perimeter and geometric variational problems : an introduction to geometric measure theory
 Responsibility
 Francesco Maggi, Universita degli Studi di Firenze, Italy.
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2012, ©2012.
 Physical description
 xix, 454 pages : illustrations ; 24 cm
 Series
 Cambridge studies in advanced mathematics ; 135.
Access
Available online
 dx.doi.org Cambridge Books Online
 proquest.safaribooksonline.com Safari Books Online
Math & Statistics Library

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QA312 .M278 2012

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QA312 .M278 2012
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Creators/Contributors
 Author/Creator
 Maggi, Francesco, 1978
Contents/Summary
 Bibliography
 Includes bibliographical references (pages [445]452) and index.
 Contents

 Part I. Radon Measures on Rn: 1. Outer measures 2. Borel and Radon measures 3. Hausdorff measures 4. Radon measures and continuous functions 5. Differentiation of Radon measures 6. Two further applications of differentiation theory 7. Lipschitz functions 8. Area formula 9. GaussGreen theorem 10. Rectifiable sets and blowups of Radon measures 11. Tangential differentiability and the area formula Part II. Sets of Finite Perimeter: 12. Sets of finite perimeter and the Direct Method 13. The coarea formula and the approximation theorem 14. The Euclidean isoperimetric problem 15. Reduced boundary and De Giorgi's structure theorem 16. Federer's theorem and comparison sets 17. First and second variation of perimeter 18. Slicing boundaries of sets of finite perimeter 19. Equilibrium shapes of liquids and sessile drops 20. Anisotropic surface energies Part III. Regularity Theory and Analysis of Singularities: 21. (LAMBDA, r0)perimeter minimizers 22. Excess and the height bound 23. The Lipschitz approximation theorem 24. The reverse Poincare inequality 25. Harmonic approximation and excess improvement 26. Iteration, partial regularity, and singular sets 27. Higher regularity theorems 28. Analysis of singularities Part IV. Minimizing Clusters: 29. Existence of minimizing clusters 30. Regularity of minimizing clusters References Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of areaminimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduatelevel textbook suitable for selfstudy and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory.
(source: Nielsen Book Data)  Supplemental links

Cover image
Contributor biographical information
Publisher description
Table of contents only
Subjects
 Subject
 Geometric measure theory.
Bibliographic information
 Publication date
 2012
 Copyright date
 2012
 Series
 Cambridge studies in advanced mathematics ; 135
 ISBN
 9781107021037 (hbk.)
 1107021030 (hbk.)