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Sets of Finite Perimeter and Geometric Variational Problems
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.
Sets of Finite Perimeter and Geometric Variational Problems
An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.
Optimal Mass Transport on Euclidean Spaces
A pedagogical introduction to the key ideas and theoretical foundation of optimal mass transport for a graduate course or self-study.
Global Regularity for Gravity Unstable Muskat Bubbles
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Fundamental Factorization of a GLSM Part I: Construction
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Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models
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Local Coefficients and Gamma Factors for Principal Series of Covering Groups
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