A finiteness principle for distance functions on Riemannian surfaces with H\'older continuous curvature

Autor:	Assouline, Rotem
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Metric Geometry
Druh dokumentu:	Working Paper
Popis:	We study distance functions from geodesics to points on Riemannian surfaces with H\"older continuous Gauss curvature, and prove a finiteness principle in the spirit of Whitney extension theory for such functions. Our result can be viewed as a finiteness principle for isometric embedding of a certain type of metric spaces into Riemannian surfaces, with control over the H\"older seminorm of the Gauss curvature. Comment: 38 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.11962 Zobrazit plný text záznamu View this record from Arxiv