The Gauss Image Problem with Weak Aleksandrov Condition

Abstract

We introduce a relaxation of the Aleksandrov condition for the Gauss Image Problem. This weaker condition turns out to be a necessary condition for two measures to be related by a convex body. We provide several properties of the new condition. A solution to the Gauss Image Problem is obtained for the case when one of the measures is assumed to be discrete and the another measure is assumed to be absolutely continuous, under the new relaxed assumption.

Final Version

References in corpus (3)

• The Logarithmic Minkowski Problem
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• The dual Minkowski problem for negative indices