论文标题
在Lipschitz上通常嵌入奇点
On Lipschitz Normally Embedded singularities
论文作者
论文摘要
任何亚分析细菌$（x，0）\ subset（\ mathbb r^n，0）$均配备两个天然指标：其外部度量，由标准的环境空间的欧几里得指标引起，其内部度量，其内部度量是通过测量胚芽$（x，0）$的最短路径长度来定义的。这两个指标等同于双形式同构的细菌（称为Lipschitz通常嵌入），在过去的十年中引起了很多兴趣。在这项调查中，我们讨论了有关Lipschitz通常嵌入奇点的许多一般事实，然后将我们的重点转移到了有关Lipschitz通常嵌入的复杂表面的标准，示例和特性的最新发展。我们结束了手稿，其中包含了我们认为值得的公开问题清单。
Any subanalytic germ $(X,0) \subset (\mathbb R^n,0)$ is equipped with two natural metrics: its outer metric, induced by the standard Euclidean metric of the ambient space, and its inner metric, which is defined by measuring the shortest length of paths on the germ $(X,0)$. The germs for which these two metrics are equivalent up to a bilipschitz homeomorphism, which are called Lipschitz Normally Embedded, have attracted a lot of interest in the last decade. In this survey we discuss many general facts about Lipschitz Normally Embedded singularities, before moving our focus to some recent developments on criteria, examples, and properties of Lipschitz Normally Embedded complex surfaces. We conclude the manuscript with a list of open questions which we believe to be worth of interest.
