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- DescriptionThe 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.
- Author BiographyFrancesco Maggi is an Associate Professor at the University of Texas, Austin, USA.
- Author(s)Francesco Maggi
- PublisherCambridge University Press
- Date of Publication09/08/2012
- Series TitleCambridge Studies in Advanced Mathematics
- Series Part/Volume Number135
- Place of PublicationCambridge
- Country of PublicationUnited Kingdom
- ImprintCambridge University Press
- Content Note90 b/w illus.
- Weight870 g
- Width152 mm
- Height228 mm
- Spine30 mm
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