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arXiv · 2106.00809

Maximal distance minimizers for a rectangle

D. D. Cherkashin·A. S. Gordeev·G. A. Strukov·Y. I. Teplitskaya
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Abstract

\emph{A maximal distance minimizer} for a given compact set $M \subset \mathbb{R}^2$ and some given $r > 0$ is a set having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset \mathbb{R}^2$ satisfying the inequality \[ \max_{y\in M} dist (y, \Sigma) \leq r. \] This paper deals with the set of maximal distance minimizers for a rectangle $M$ and small enough $r$.

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D. D. Cherkashin, A. S. Gordeev, G. A. Strukov, Y. I. Teplitskaya. 2021-06-01. Maximal distance minimizers for a rectangle. https://arxiv.org/abs/2106.00809

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