On the extendability by continuity of angular valuations on polytopes
Metric Geometry
2019-08-15 v2
Abstract
A classical theorem of P. McMullen describes all valuations on polytopes that are invariant under translations and weakly continuous, i.e., continuous with respect to parallel displacements of the facets of a polytope. While it is typically not difficult to check that a valuation is weakly continuous, it is not clear how to decide whether it admits a continuous extension to convex bodies. In a special case of McMullen's construction a simple necessary and sufficient condition on the initial data of such an extension is obtained.
Keywords
Cite
@article{arxiv.1907.11606,
title = {On the extendability by continuity of angular valuations on polytopes},
author = {Thomas Wannerer},
journal= {arXiv preprint arXiv:1907.11606},
year = {2019}
}