Uniqueness of solutions to the logarithmic Minkowski problem in ℝ³

2022/02/21 by Chen, Shibing, Feng, Yibin, Liu, Weiru
#52A20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.10074

Abstract

In this paper, we prove the uniqueness of solutions to the logarithmic Minkowski problem in ℝ³ without symmetry condition, provided the density of the measure is close to 1 in C^α norm. This result also implies the uniqueness of self-similar solutions to the anisotropic Gauss curvature flow in ℝ³ when the speed function is C^α close to a positive constant.

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