H\"older continuity for support measures of convex bodies
Metric Geometry
2015-01-27 v1
Abstract
The support measures of a convex body are a common generalization of the curvature measures and the area measures. With respect to the Hausdorff metric on the space of convex bodies, they are weakly continuous. We provide a quantitative improvement of this result, by establishing a H\"older estimate for the support measures in terms of the bounded Lipschitz metric, which metrizes the weak convergence. Specializing the result to area measures yields a reverse counterpart to earlier stability estimates, concerning Minkowski's existence theorem for convex bodies with given area measure.
Keywords
Cite
@article{arxiv.1501.06214,
title = {H\"older continuity for support measures of convex bodies},
author = {Daniel Hug and Rolf Schneider},
journal= {arXiv preprint arXiv:1501.06214},
year = {2015}
}
Comments
The manuscript is an extended and improved version of the second part of the manuscript number arxiv:1310.1514