Calculus of Variations and Geometric Measure Theory

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

Maximal distance minimizers for a rectangle

created by teplitskaya1 on 06 Jun 2021



Inserted: 6 jun 2021
Last Updated: 6 jun 2021

Year: 2021

ArXiv: 2106.00809 PDF


\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 $r$.