Minkowski Problems for Geometric Measures
Yong Huang, Deane Yang, and Gaoyang Zhzng
TL;DR
This paper surveys the development of Minkowski problems for geometric measures, highlighting their role in convex geometry, PDEs, and harmonic analysis within the Brunn-Minkowski framework.
Contribution
It provides a comprehensive overview of classical and recent Minkowski problems, integrating various mathematical disciplines and presenting a unified conceptual framework.
Findings
Extensive development of Minkowski problems in convex geometry
Connections established with PDEs and harmonic analysis
Structured overview of the Brunn-Minkowski theory and its extensions
Abstract
This paper describes the theory of Minkowski problems for geometric measures in convex geometric analysis. The theory goes back to Minkowski and Aleksandrov and has been developed extensively in recent years. The paper surveys classical and new Minkowski problems studied in convex geometry, PDEs, and harmonic analysis, and structured in a conceptual framework of the Brunn-Minkowski theory, its extensions, and related subjects.
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Taxonomy
TopicsRelativity and Gravitational Theory · Geometric Analysis and Curvature Flows · Point processes and geometric inequalities