On the total perimeter of disjoint convex bodies

Authors

Arseniy Akopyan
Alexey Glazyrin, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2023

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 k convex planar bodies with disjoint interiors contained in a convex body of perimeter p and diameter d is not greater than p+2(k−1)d.

Recommended Citation

Akopyan, Arseniy, and Alexey Glazyrin. "On the total perimeter of disjoint convex bodies." arXiv preprint arXiv:2308.16340 (2023).