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arXiv · 1501.06214

Hölder continuity for support measures of convex bodies

Daniel Hug·Rolf Schneider
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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 Hölder 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.

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Daniel Hug, Rolf Schneider. 2015-01-25. Hölder continuity for support measures of convex bodies. https://doi.org/10.1007/s00013-014-0719-0

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