Equidistant sets on Alexandrov surfaces
Metric Geometry
2022-05-20 v1
Abstract
We examine properties of equidistant sets determined by nonempty disjoint compact subsets of a compact 2-dimensional Alexandrov space (of curvature bounded below). The work here generalizes many of the known results for equidistant sets determined by two distinct points on a compact Riemannian 2-manifold. Notably, we find that the equidistant set is always a finite simplicial 1-complex. These results are applied to answer an open question concerning the Hausdorff dimension of equidistant sets in the Euclidean plane.
Keywords
Cite
@article{arxiv.2205.09155,
title = {Equidistant sets on Alexandrov surfaces},
author = {Logan S. Fox and J. J. P. Veerman},
journal= {arXiv preprint arXiv:2205.09155},
year = {2022}
}