亚历山德罗夫曲面上的等距集

Pub Date : 2023-10-01 DOI:10.1016/j.difgeo.2023.102042

Logan S. Fox, J.J.P. Veerman

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引用次数: 1

摘要

我们研究了由紧致2维Alexandrov空间(曲率有界)的非空不相交紧致子集确定的等距集的性质。本文的工作推广了由紧黎曼2-流形上两个不同点确定的等距集的许多已知结果。值得注意的是，我们发现等距集总是一个有限的简单1-复集。这些结果被用来回答关于欧几里得平面上等距集合的豪斯多夫维数的一个开放性问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Equidistant sets on Alexandrov surfaces

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.

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