A new proof of the Wulff-Gage isoperimetric inequality and its applications

2023/11/29 by Lei Ma, Ma, Lei, Chunna Zeng +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Inequalities and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2311.17505

openalex publication_date 2023/11/29 · openalex created_date 2023/12/01 · openalex updated_date 2026/07/28

Abstract

A new proof of the Wulff-Gage isoperimetric inequality for origin-symmetric convex bodies is provided. As its applications, we prove the uniqueness of log-Minkowski problem and a new proof of the log-Minkowski inequality of curvature entropy for origin-symmetric convex bodies of C² boundaries in \mathbb R² is given.

Related

• The log-Minkowski inequality of curvature entropy for non-symmetric convex bodies
• Brunn-Minkowski and Reverse Isoperimetric Inequalities for Dual Quermassintegrals
• Anisotropic Isoperimetric Inequalities involving Boundary Momentum, Perimeter and Volume
• The L_p-floating area, curvature entropy, and isoperimetric inequalities on the sphere
• On a reverse isoperimetric inequality for relative outer parallel bodies