English

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 Y=YεY=Y_\varepsilon 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.

Keywords

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}
}