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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.
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Katarzyna Charytanowicz, Waldemar Cieślak, Witold Mozgawa, A generalization of the total mean curvature. Rend. Sem. Mat. Univ. Padova 146 (2021), pp. 223–231DOI 10.4171/RSMUP/87