## D. D. Cherkashin - A. S. Gordeev - G. A. Strukov - Y. Teplitskaya

# Maximal distance minimizers for a rectangle

created by teplitskaya1 on 06 Jun 2021

[

BibTeX]

*preprint*

**Inserted:** 6 jun 2021

**Last Updated:** 6 jun 2021

**Year:** 2021

**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 $r$.