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arXiv · 2202.10074

Uniqueness of solutions to the logarithmic Minkowski problem in $\mathbb{R}^3$

Shibing Chen·Yibin Feng·Weiru Liu
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Abstract

In this paper, we prove the uniqueness of solutions to the logarithmic Minkowski problem in $\mathbb{R}^3$ without symmetry condition, provided the density of the measure is close to $1$ in $C^{\alpha}$ norm. This result also implies the uniqueness of self-similar solutions to the anisotropic Gauss curvature flow in $\mathbb{R}^3$ when the speed function is $C^{\alpha}$ close to a positive constant.

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Shibing Chen, Yibin Feng, Weiru Liu. 2022-02-21. Uniqueness of solutions to the logarithmic Minkowski problem in $\mathbb{R}^3$. https://arxiv.org/abs/2202.10074

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