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On the planar Gaussian-Minkowski problem

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arxiv 2303.17389 v1 pith:HLVVI34J submitted 2023-03-30 math.MG math.AP

Shibing Chen , Shengnan Hu , Weiru Liu , Yiming Zhao This is my paper · ORCID
classification math.MGmath.AP
keywords gaussian-minkowskiproblemmeasureapplicationapproachareabodycentered
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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.

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  1. Compactness of the $L_p$ dual Minkowski problem in $\mathbb{R}^3$

    math.AP 2025-05 conditional novelty 7.0 of 10

    For convex bodies in R^3, bounded L_p qth dual curvature with p in [0,1) and q>2+p forces a uniform diameter upper bound and volume lower bound.

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