A generalization of the total mean curvature

2019/12/23 by Charytanowicz, Katarzyna, Cieslak, Waldemar, Mozgawa, Witold
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.10662

Abstract

A special formula for the total mean curvature of an ovaloid is derived. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, some integral formula for ovaloids is proved.

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