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Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory

Francesco Maggi, Universita degli Studi di Firenze, Italy
Cambridge : Cambridge University Press, 2012.
Cambridge studies in advanced mathematics
9781107021037, 1107021030
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"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 area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory"--
Machine generated contents note: 1. Radon measures on Rn; 2. Sets of finite perimeter; 3. Regularity theory and analysis of singularities; 4. Minimizing clusters.
xix, 454 pages : illustrations ; 24 cm
Includes bibliographical references and index.
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Cambridge studies in advanced mathematics ; 135
Cambridge studies in advanced mathematics 135
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