TL;DR
This paper extends the Master Steiner formula to conic support measures, demonstrating their Hölder continuity and providing tools for analyzing convex cones in geometric measure theory.
Contribution
It introduces an extension of the Master Steiner formula to conic support measures and proves their Hölder continuity under specific metrics.
Findings
Extended the Master Steiner formula to conic support measures
Proved Hölder continuity of conic support measures
Established metrics for weak convergence of conic support measures
Abstract
The conic support measures localize the conic intrinsic volumes of closed convex cones in the same way as the support measures of convex bodies localize the intrinsic volumes of convex bodies. In this note, we extend the `Master Steiner formula' of McCoy and Tropp, which involves conic intrinsic volumes, to conic support measures. Then we prove H\"{o}lder continuity of the conic support measures with respect to the angular Hausdorff metric on convex cones and a metric on conic support measures which metrizes the weak convergence.
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematical Inequalities and Applications · Pharmacological Effects of Medicinal Plants