A generalization of the total mean curvature

TL;DR

This paper derives a new formula for total mean curvature of ovaloids, extending the concept to boundaries of strictly convex sets and providing integral formulas for ovaloids.

Contribution

It introduces a generalized formula for total mean curvature applicable to strictly convex boundaries, expanding the theoretical framework.

Findings

Derived a special formula for total mean curvature of ovaloids

Extended the notion of mean curvature to strictly convex set boundaries

Proved integral formulas for ovaloids

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.