The $L_p$-Gaussian Minkowski problem

TL;DR

This paper extends the Gaussian Minkowski problem to the $L_p$ setting, establishing existence and uniqueness of symmetric solutions for $p \, \geq \, 1$, advancing the understanding of convex geometric problems in Gaussian spaces.

Contribution

It introduces the $L_p$-Gaussian Minkowski problem and proves the existence and uniqueness of symmetric solutions for $p \, \geq \, 1$, expanding prior work in Gaussian convex geometry.

Findings

Proved existence of symmetric solutions for the $L_p$-Gaussian Minkowski problem.

Established uniqueness of solutions in the symmetric case for $p \, \geq \, 1$.

Extended classical Minkowski problem results to Gaussian probability spaces.

Abstract

In this paper, we extend the article that Minkowski problem in Gaussian probability space of Huang et al. to $L_p$-Gaussian Minkowski problem, and obtain the existence and uniqueness of $o$-symmetry weak solution in case of $p\geq1$.