A Lower Estimate for the Modified Steiner Functional

TL;DR

This paper establishes a new inequality for the modified Steiner functional, extending the integral of mean curvature for convex surfaces, and provides an integral representation over intersecting hyperplanes.

Contribution

It introduces a lower bound inequality for the modified Steiner functional and derives an integral expression involving hyperplanes intersecting the surface.

Findings

Proved inequality (1) for A(M)

Derived an integral expression for A(M) over hyperplanes

Extended the notion of mean curvature integral for convex surfaces

Abstract

We prove inequality (1) for the modified Steiner functional A(M), which extends the notion of the integral of mean curvature for convex surfaces.We also establish an exression for A(M) in terms of an integral over all hyperplanes intersecting the polyhedralral surface M.