An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers. Series: Cambridge Studies in Advanced Mathematics. Num Pages: 480 pages, 90 b/w illus. BIC Classification: PBKL; PBMS. Category: (P) Professional & Vocational. Dimension: 157 x 230 x 29. Weight in Grams: 802. An Introduction to Geometric Measure Theory. Series: Cambridge Studies in Advanced Mathematics. 480 pages, 90 b/w illus. An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers. Cateogry: (P) Professional & Vocational. BIC Classification: PBKL; PBMS. Dimension: 157 x 230 x 29. Weight: 802. . 2012. 1st Edition. Hardcover. . . . .

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Bibliographic Details

Title

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

Publisher

Cambridge University Press

Publication Date

2012

Language

English

ISBN 10

1107021030

ISBN 13

9781107021037

Binding

Hardcover

Edition

1st Edition

Condition

New

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About this title

Synopsis

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.

About the Author

Francesco Maggi is a Professor of Mathematics at the University of Texas, Austin, USA.

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