The even Lp Gaussian dual Minkowski problem

TL;DR

This paper addresses the even Lp Gaussian dual Minkowski problem for p>1, establishing the existence of symmetric solutions, thereby advancing the understanding of geometric measure problems related to convex bodies.

Contribution

It proves the existence of o-symmetric solutions for the even Lp Gaussian dual Minkowski problem when p>1, filling a gap in the theory for this class of problems.

Findings

Existence of o-symmetric solutions for p>1

Extension of the Gaussian dual Minkowski problem to Lp setting

Advancement in geometric measure theory for convex bodies

Abstract

The even Gaussian dual Minkowski problem studied by Feng, Hu and Xu, In this paper, we consider the even $L_p$ dual-Gaussian Minkowski problem for $p>1$. The existence of $o$-symmetric solution in the case $p>1$ is obtained.