• Corpus ID: 235294054

# Maximal distance minimizers for a rectangle

@inproceedings{Cherkashin2021MaximalDM,
title={Maximal distance minimizers for a rectangle},
author={Danila D. Cherkashin and Alexey Gordeev and G. A. Strukov and Yana Teplitskaya},
year={2021}
}
• Published 1 June 2021
• Mathematics
A maximal distance minimizer for a given compact set M ⊂ R and some given r > 0 is a set having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets Σ ⊂ R 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.

## References

SHOWING 1-10 OF 17 REFERENCES
Regularity of Maximum Distance Minimizers
We study properties of sets having the minimum length (one-dimensional Hausdorff measure) in the class of closed connected sets Σ ⊂ ℝ2 satisfying the inequality maxyϵM dist (y, Σ) ≤ r for a given
Qualitative Properties of Maximum Distance Minimizers and Average Distance Minimizers in Rn
• Mathematics
• 2004
AbstractWe consider one-dimensional networks of finite length in $$\mathbb{R}^n$$ minimizing the average distance functional and the maximum distance functional subject to the length constraint.
On regularity of maximal distance minimizers
This work shows that a maximal distance minimizer is isotopic to a finite Steiner tree even for a "bad" compact $M$, which differs it from a solution of the Steiner problem.
On minimizers of the maximal distance functional for a planar convex closed smooth curve.
• Mathematics
• 2020
Fix a compact $M \subset \mathbb{R}^2$ and $r>0$. A minimizer of the maximal distance functional is a connected set $\Sigma$ of the minimal length, such that \[ max_{y \in M} dist(y,\Sigma) \leq r.
Optimal Transportation Problems with Free Dirichlet Regions
• Mathematics
• 2002
A Dirichlet region for an optimal mass transportation problem is, roughly speaking, a zone in which the transportation cost is vanishing. We study the optimal transportation problem with an unknown
On the horseshoe conjecture for maximal distance minimizers
• Mathematics
• 2015
We study the properties of sets $\Sigma$ having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset \mathbb{R}^2$ satisfying the inequality
On one-dimensional continua uniformly approximating planar sets
• Mathematics
• 2006
AbstractConsider the class of closed connected sets $$\Sigma\subset {\cal R}^n$$ satisfying length constraint $${\cal H}(\Sigma)\leq l$$ with given l>0. The paper is concerned with the properties of
Steiner Minimal Trees
• Mathematics
• 2005
On the problem of Steiner
There is a well-known elementary problem: (S3) Given a triangle T with the vertices a1, a2, a3, to find in the plane of T the point p which minimize s the sum of the distances |pa1| + |pa2| + |pa3|.
C-Xsc: A C++ Class Library for Extended Scientific Computing
• Computer Science
• 1993
This chapter discusses C-XSC, a Programming Environment for Scientific Computing with Result Verification with a focus on C and C++, and some of the techniques used to develop these languages.