Calculus of Variations and Geometric Measure Theory

D. Cherkashin - Y. Teplitskaya

An overview of maximal distance minimizers problem

created by teplitskaya1 on 10 Feb 2023
modified by cherkashin on 12 Feb 2024



Inserted: 10 feb 2023
Last Updated: 12 feb 2024

Year: 2022

ArXiv: 2212.05607 PDF


Consider a compact $M \subset \mathbb{R}^d$ and $l > 0$. A maximal distance minimizer problem is to find a connected compact set $\Sigma$ of the length (one-dimensional Hausdorff measure $\mathcal{H}^1$) at most $l$ that minimizes \[ \max_{y \in M} dist (y, \Sigma), \] where $dist$ stands for the Euclidean distance. We give a survey on the results on the maximal distance minimizers and related problems.

Keywords: maximal distance minimizer