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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.05607 |
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Table of Contents:
- Consider a compact $M \subset \mathbb{R}^d$ and $l > 0$. A maximal distance minimizer problem is to find a connected compact set $Σ$ of the length (one-dimensional Hausdorff measure $\mathcal H$) at most $l$ that minimizes \[ \max_{y \in M} dist (y, Σ), \] where $dist$ stands for the Euclidean distance. We give a survey on the results on the maximal distance minimizers and related problems. Also we fill some natural gaps by showing NP-hardness of the maximal distance minimizing problem, establishing its $Γ$-convergence, considering the penalized form and discussing uniqueness of a solution. We finish with open questions.