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Singular sets of convex bodies and surfaces with generalized curvatures

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Abstract

In this paper we consider generalized surfaces with curvature measures and we study the properties of those k-dimensional subsets Σk of such surfaces where the curvatures have positive density with respect to k-dimensional Hausdorff measure. Special attention is given to boundaries of convex bodies inR 3. We introduce a class of convex sets whose curvatures live only on integer dimension sets. For such convex sets we consider integral functionals depending on the curvature and the area ofK and on the curvature andH k of Σk.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, 38050, Povo (Trento), Italy

    G. Anzellotti & E. Ossanna

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  1. G. Anzellotti
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  2. E. Ossanna
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Anzellotti, G., Ossanna, E. Singular sets of convex bodies and surfaces with generalized curvatures. Manuscripta Math 86, 417–433 (1995). https://doi.org/10.1007/BF02568003

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  • DOI: https://doi.org/10.1007/BF02568003

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