On the planar Gaussian-Minkowski problem
Metric Geometry
2023-03-31 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2303.17389,
title = {On the planar Gaussian-Minkowski problem},
author = {Shibing Chen and Shengnan Hu and Weiru Liu and Yiming Zhao},
journal= {arXiv preprint arXiv:2303.17389},
year = {2023}
}