The Minkowski problem in the Gaussian probability space

TL;DR

This paper investigates the Gaussian Minkowski problem, establishing existence and uniqueness results in the Gaussian probability space, advancing the understanding of convex geometry under Gaussian measures.

Contribution

It provides the first comprehensive existence and uniqueness results for the unnormalized Gaussian Minkowski problem, extending classical convex geometric analysis to Gaussian spaces.

Findings

Existence of solutions for the Gaussian Minkowski problem.

Uniqueness of solutions under certain conditions.

Extension of classical Minkowski problem results to Gaussian measures.

Abstract

The Minkowski problem in Gaussian probability space is studied in this paper. In addition to providing an existence result on a Gaussian-volume-normalized version of this problem, the main goal of the current work is to provide uniqueness and existence results on the Gaussian Minkowski problem (with no normalization required).