On the total perimeter of disjoint convex bodies

Arseniy Akopyan; Alexey Glazyrin

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arXiv · 2308.16340

On the total perimeter of disjoint convex bodies

Arseniy Akopyan·Alexey Glazyrin

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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 $p+2(k-1)d$.

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Arseniy Akopyan, Alexey Glazyrin. 2023-08-30. On the total perimeter of disjoint convex bodies. https://arxiv.org/abs/2308.16340

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