|
中图分类法:
|
O174.12 版次： |
|
著者:
|
Maggi, Francesco, |
|
题名:
|
Sets of finite perimeter and geometric variational problems : [ an introduction to geometric measure theory /] / , |
|
出版发行:
|
出版地： New York : 出版社： Cambridge University Press, 出版日期： 2012. |
|
载体形态:
|
xix, 454 pages ; 24 cm. |
|
内容提要:
|
"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. 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"-- |
|
主题词:
|
Geometric measure theory. |
|
索书号:
|
1 |