The Minkowski problem in the Gaussian probability space

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).

arXiv commentupdated introduction and bibliography

References in corpus (9)

• The Logarithmic Minkowski Problem
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• General affine surface areas
• Crofton measures and Minkowski valuations
• Relative entropy of cone measures and $L_p$ centroid bodies
• The dual Minkowski problem for negative indices
• The $L_p$-Minkowski problem for $-n<p<1$
• On some inequalities for Gaussian measures
• The equality cases of the Ehrhard-Borell inequality