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 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.
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