Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
Metric Geometry
2025-02-11 v1
Abstract
A longstanding question in the dual Brunn-Minkowski theory is what are the dual analogues of Federer's curvature measures for convex bodies. The answer to this is provided. This leads naturally to dual versions of Minkowski-type problems, which answer the question of what are necessary and sufficient conditions for a Borel measure to be a dual curvature measure of a convex body. Sufficient conditions, involving measure concentration, are established for the existence of solutions to these problems.
Keywords
Cite
@article{arxiv.2502.05436,
title = {Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems},
author = {Yong Huang and Erwin Lutwak and Deane Yang and Gaoyong Zhang},
journal= {arXiv preprint arXiv:2502.05436},
year = {2025}
}