TY  - BOOK
AU  - Maggi,Francesco
TI  - Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory 
T2  - Cambridge Studies in Advanced Mathematics
SN  - 9781139108133 (ebook)
AV  - QA312 .M278 2012
U1  - 515/.42 23
PY  - 2012///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Geometric measure theory
N1  - Title from publisher's bibliographic system (viewed on 04 Apr 2016)
N2  - 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
UR  - http://dx.doi.org/10.1017/CBO9781139108133
ER  -