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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
Format
Book
Published
Cambridge : Cambridge University Press, 2012.
Language
English
Series
Cambridge studies in advanced mathematics
ISBN
9781107021037, 1107021030
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Publisher description
Table of contents only
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 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"--
Contents
Machine generated contents note: 1. Radon measures on Rn; 2. Sets of finite perimeter; 3. Regularity theory and analysis of singularities; 4. Minimizing clusters.
Description
xix, 454 pages : illustrations ; 24 cm
Notes
Includes bibliographical references and index.
Series Statement
Cambridge studies in advanced mathematics ; 135
Cambridge studies in advanced mathematics 135
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