Maximal distance minimizers for a rectangle

2021/06/01 by Cherkashin, D. D., Gordeev, A. S., Strukov, G. A. +1 · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2106.00809

Abstract

A maximal distance minimizer for a given compact set M ⊂ ℝ² and some given r > 0 is a set having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets Σ⊂ ℝ² satisfying the inequality max_{y∈ M} dist (y, Σ) ≤ r. This paper deals with the set of maximal distance minimizers for a rectangle M and small enough r.

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