On the planar Gaussian-Minkowski problem

2023/03/30 by Shibing Chen, Shengnan Hu, Chen, Shibing +5 · 3 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2303.17389

openalex publication_date 2023/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The current work focuses on the Gaussian-Minkowski problem in dimension 2. In particular, we show that if the Gaussian surface area measure is proportional to the spherical Lebesgue measure, then the corresponding convex body has to be a centered disk. As an application, this ``uniqueness'' result is used to prove the existence of smooth small solutions to the Gaussian-Minkowski problem via a degree-theoretic approach.

Cited by

• On The Minkowski Problem With Respect To A Mixed Euclidean-Gaussian Density
• Uniqueness of S₂-isotropic solutions to the isotropic L_p Minkowski problem
• The Gaussian Minkowski problem for epigraphs of convex functions

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