English

Global bi-Lipschitz classification of semi-algebraic surfaces

Differential Geometry 2022-12-14 v1 Algebraic Geometry Metric Geometry

Abstract

We classify semi-algebraic surfaces in Rn\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.

Keywords

Cite

@article{arxiv.2212.06306,
  title  = {Global bi-Lipschitz classification of semi-algebraic surfaces},
  author = {Alexandre Fernandes and José Edson Sampaio},
  journal= {arXiv preprint arXiv:2212.06306},
  year   = {2022}
}

Comments

20 pages and 2 figures

R2 v1 2026-06-28T07:31:52.421Z