论文标题
Alexandrov表面上的等距集
Equidistant sets on Alexandrov surfaces
论文作者
论文摘要
我们检查了由紧凑型二维Alexandrov空间（下面有弯曲的曲率）的非平整脱节紧凑子集确定的等距集的属性。这里的工作概括了许多已知结果，用于由紧凑的Riemannian 2-manifold上的两个不同点确定的等距集。值得注意的是，我们发现等距集始终是有限的简单1复合物。这些结果用于回答有关欧几里得平面中等距集的Hausdorff尺寸的一个开放问题。
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.
