Polyhedral Gauss-Bonnet theorems and valuations
Metric Geometry
2017-08-18 v1
Abstract
The Gauss-Bonnet theorem for a polyhedron (a union of finitely many compact convex polytopes) in -dimensional Euclidean space expresses the Euler characteristic of the polyhedron as a sum of certain curvatures, which are different from zero only at the vertices of the polyhedron. This note suggests a generalization of these polyhedral vertex curvatures, based on valuations, and thus obtains a variety of polyhedral Gauss-Bonnet theorems.
Cite
@article{arxiv.1708.05213,
title = {Polyhedral Gauss-Bonnet theorems and valuations},
author = {Rolf Schneider},
journal= {arXiv preprint arXiv:1708.05213},
year = {2017}
}