JournalsrsmupVol. 146pp. 223–231

A generalization of the total mean curvature

  • Katarzyna Charytanowicz

    Maria Curie-Skłodowska University, Lublin, Poland

  • Waldemar Cieślak

    State School of Higher Education in Chełm, Poland

  • Witold Mozgawa

    Maria Curie-Skłodowska University, Lublin, Poland
A generalization of the total mean curvature cover
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Abstract

We derive a special formula for the total mean curvature of an ovaloid. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, an integral formula is proved.

Cite this article

Katarzyna Charytanowicz, Waldemar Cieślak, Witold Mozgawa, A generalization of the total mean curvature. Rend. Sem. Mat. Univ. Padova 146 (2021), pp. 223–231

DOI 10.4171/RSMUP/87