关于 Lipschitz 正规嵌入集合的链环
代数几何
2023-03-30 v3 度量几何
摘要
中的道路连通次解析子集自然配备两种度量：内度量与外度量。若这两种度量等价，则称该子集为 Lipschitz 正规嵌入（LNE）。本文给出次解析集为 LNE 的一些判别准则。一个基本问题是 LNE 性质是否为锥性的，即能否用次解析集芽的链环的性质来描述其 LNE 性质。我们通过引入称为链环 Lipschitz 正规嵌入的新概念来回答此问题。我们证明了在链环连通的集合情形下，该概念与 LNE 概念等价。
关键词
引用
@article{arxiv.2101.05572,
title = {On the link of Lipschitz normally embedded sets},
author = {Rodrigo Mendes and José Edson Sampaio},
journal= {arXiv preprint arXiv:2101.05572},
year = {2023}
}
备注
The previous version had two sets of different results. We have divided our pre-print into two, and this version contains the first set of results, which was sections 1-4. The second part, which was Section 5, will appear in a new arXiv submission. The title was changed