The Logarithmic Minkowski conjecture and the L_p-Minkowski Problem

2022/10/01 by Károly J. Böröczky, Boroczky, Karoly J. · 7 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · doi:10.48550/arxiv.2210.00194

openalex publication_date 2022/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The current state of art concerning the L_p Minkowski problem as a Monge-Ampere equation on the sphere and Lutwak's Logarithmic Minkowski conjecture about the uniqueness of even solution in the p=0 case are surveyed and connections to many related problems are discussed.

Cited by

• On the uniqueness of even L^p Minkowski problem
• Monotonicity of the deficit in the local log-Brunn-Minkowski inequality
• The capillary Gauss curvature flow
• Uniqueness of S₂-isotropic solutions to the isotropic L_p Minkowski problem
• Functional Liftings of Restricted Geometric Inequalities
• On p-Brunn-Minkowski and Brascamp-Lieb inequalities
• On polynomial inequalities for cone-volumes of polytopes

Related

• Non-uniqueness of solutions to the dual L_p-Minkowski problem
• The planar L_p-Minkowski problem for 0< p<1
• The discrete logarithmic Minkowski problem for the electrostatic \mathfrakp-capacity
• Stable solution of the log-Minkowski problem in the case of many hyperplane symmetries
• The discrete logarithmic Minkowski problem