论文标题
Lipschitz真实半ge表面的几何形状
Lipschitz Geometry of Real Semialgebraic Surfaces
论文作者
论文摘要
我们在这里介绍了Lipschitz的基本结果，该结果是半缘表面细菌的几何形状。尽管很久以前就解决了表面细菌相对于内部度量的Bi-Lipschitz分类问题，但相对于外部度量的分类仍然是一个开放的问题。我们回顾了与表面细菌的外部和环境Bi-Lipschitz分类有关的最新结果。特别是，我们解释了为什么外Lipschitz分类要比内部分类要难得多，以及为什么表面细菌的环境Lipschitz几何形状与它们的外Lipschitz几何形状大不相同。特别是，我们表明表面细菌的环境Lipschitz几何形状包括所有结理论。
We present here basic results in Lipschitz Geometry of semialgebraic surface germs. Although bi-Lipschitz classification problem of surface germs with respect to the inner metric was solved long ago, classification with respect to the outer metric remains an open problem. We review recent results related to the outer and ambient bi-Lipschitz classification of surface germs. In particular, we explain why the outer Lipschitz classification is much harder than the inner classification, and why the ambient Lipschitz Geometry of surface germs is very different from their outer Lipschitz Geometry. In particular, we show that the ambient Lipschitz Geometry of surface germs includes all of the Knot Theory.
