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arXiv · 2212.06306

Global bi-Lipschitz classification of semi-algebraic surfaces

Alexandre Fernandes·José Edson Sampaio
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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.

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Alexandre Fernandes, José Edson Sampaio. 2022-12-13. Global bi-Lipschitz classification of semi-algebraic surfaces. https://arxiv.org/abs/2212.06306

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