On the Total Perimeter of Pairwise Disjoint Convex Bodies

Authors

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

Document Type

Article

Publication Date

11-21-2024

Abstract

In this note we introduce a pseudometric on closed convex planar curves based on distances between normal lines and show its basic properties. Then we use this pseudometric to give a shorter 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.

Comments

Original published version available at https://doi.org/10.1556/012.2024.04317

Recommended Citation

Akopyan, Arseniy, and Alexey Glazyrin. "On the Total Perimeter of Pairwise Disjoint Convex Bodies", Studia Scientiarum Mathematicarum Hungarica 61, 3 (2024): 237-250. https://doi.org/10.1556/012.2024.04317

Publication Title

Studia Scientiarum Mathematicarum Hungarica

DOI

https://doi.org/10.1556/012.2024.04317