On the planar Gaussian-Minkowski problem
On the planar Gaussian-Minkowski problem
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DOI：
10.1016/j.aim.2023.109351
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发表时间：
2023-03
影响因子：
1.7
通讯作者：
Shibing Chen;Shengnan Hu;Weiru Liu;Yiming Zhao
中科院分区：
文献类型：
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作者：
Shibing Chen;Shengnan Hu;Weiru Liu;Yiming Zhao
目前的工作主要集中在二维的高斯-闵可夫斯基问题上。特别地，我们证明了如果高斯表面积测度与球面勒贝格测度成正比，那么相应的凸体必须是一个中心圆盘。作为应用，利用该“唯一性”结果，利用度理论方法证明了高斯-闵可夫斯基问题光滑小解的存在性。
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.