论文标题
$ \ mathbb {r}^3 $中对数Minkowski问题的解决方案的唯一性
Uniqueness of solutions to the logarithmic Minkowski problem in $\mathbb{R}^3$
论文作者
论文摘要
在本文中，我们证明了对数Minkowski问题的独特性，只要该度量的密度接近$ C^α$ norm，$ \ Mathbb {r}^3 $没有对称条件。该结果也意味着自相似的解决方案对各向异性高斯曲率流的独特性，当时$ \ mathbb {r}^3 $当速度函数为$ c^α$接近正常数时。
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 $C^α$ 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 $C^α$ close to a positive constant.
