Global bi-Lipschitz classification of semialgebraic surfaces

A. Fernandes, J. E. Sampaio
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引用次数: 2

Abstract

We classify semi-algebraic surfaces in $\mathbb{R}^n$ with isolated singularities up to bi-Lipschitz homeomorphisms with respect to the inner distance. In particular, we obtain complete classifications for the Nash surfaces and the complex algebraic curves. We also address the minimal surfaces with finite total curvature.
半代数曲面的全局bi-Lipschitz分类
我们对$\mathbb{R}^n$中具有孤立奇点直至关于内距的双lipschitz同胚的半代数曲面进行了分类。特别地,我们得到了纳什曲面和复杂代数曲线的完全分类。我们还讨论了具有有限总曲率的最小曲面。
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