The Gaussian-Minkowski problem for $C$-pseudo-cones

TL;DR

This paper investigates the Gaussian surface area measures for $C$-pseudo-cones, establishing the existence of solutions to the Gaussian-Minkowski problem under certain conditions using variational and approximation techniques.

Contribution

It introduces the first existence results for the Gaussian-Minkowski problem specifically for $C$-pseudo-cones with small co-volume.

Findings

Existence of solutions for the Gaussian-Minkowski problem for $C$-pseudo-cones.

Application of variational and approximation methods in this context.

Extension of classical Minkowski problem techniques to $C$-pseudo-cones.

Abstract

The Gaussian surface area measures for $C$-pseudo-cones are studied in this paper. Using the variational arguments and the approximation methods of Schneider, we obtain the existence of solutions to the Gaussian-Minkowski problem for $C$-pseudo-cones with small co-volume.