Surface area deviation between smooth convex bodies and polytopes
Metric Geometry
2018-11-13 v1 Probability
Abstract
The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope with a given number of vertices is studied. The paper considers the case where the deviation is measured in terms of the surface areas of the involved sets, more precisely, by what is called the surface area deviation. The proof uses arguments and constructions from probability, convex and integral geometry. The bound is closely related to -affine surface areas.
Keywords
Cite
@article{arxiv.1811.04656,
title = {Surface area deviation between smooth convex bodies and polytopes},
author = {Julian Grote and Christoph Thaele and Elisabeth M. Werner},
journal= {arXiv preprint arXiv:1811.04656},
year = {2018}
}