Maximal distance minimizers for a rectangle
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 $r$.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.00809
- arXiv:
- arXiv:2106.00809
- Bibcode:
- 2021arXiv210600809C
- Keywords:
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- Mathematics - Metric Geometry;
- Mathematics - Optimization and Control
- E-Print:
- 25p, 17f