Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature
Differential Geometry
2023-03-24 v2
Abstract
We approximate boundaries of convex polytopes by smooth hypersurfaces with {\it positive mean curvatures} and, by using basic geometric relations between the scalar curvatures of Riemannin manifolds and the mean curvatures of their boundaries, establish {\it lower bound on the dihedral angles} of these polytopes.
Cite
@article{arxiv.2207.13346,
title = {Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature},
author = {Misha Gromov},
journal= {arXiv preprint arXiv:2207.13346},
year = {2023}
}