Sets of finite perimeter and geometric variational problems : an introduction to geometric measure theory /
Sets of Finite Perimeter & Geometric Variational Problems
Francesco Maggi, Università degli Studi di Firenze, Italy.
- Cambridge : Cambridge University Press, 2012.
- 1 online resource (xix, 454 pages) : digital, PDF file(s).
- Cambridge studies in advanced mathematics ; 135 .
- Cambridge studies in advanced mathematics ; 135. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.