Curvatures for unions of WDC sets

2019/09/16 by Dušan Pokorný, Pokorný, Dušan · 1 citation
Engineering · #53C65 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1909.07119

openalex publication_date 2019/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of the curvature measures for a class of \cal U_{\rm WDC} sets, which is a direct generalization of \cal U_{\rm PR} sets studied by Rataj and Zähle. Moreover, we provide a simple characterisation of \cal U_{\rm WDC} sets in \mathbb R² and prove that in \mathbb R² the class of \cal U_{\rm WDC} sets contains essentially all classes of sets known to admit curvature measures.

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