On the total perimeter of disjoint convex bodies
Metric Geometry
2023-09-01 v1 Combinatorics
Abstract
In this note we introduce a pseudometric on convex planar curves based on distances between normal lines and show its basic properties. Then we use this pseudometric to give a short proof of the theorem by Pinchasi that the sum of perimeters of convex planar bodies with disjoint interiors contained in a convex body of perimeter and diameter is not greater than .
Cite
@article{arxiv.2308.16340,
title = {On the total perimeter of disjoint convex bodies},
author = {Arseniy Akopyan and Alexey Glazyrin},
journal= {arXiv preprint arXiv:2308.16340},
year = {2023}
}