Approximate control of the marked length spectrum by short geodesics

Autor:	Butt, Karen
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	The marked length spectrum (MLS) of a closed negatively curved manifold $(M, g)$ is known to determine the metric $g$ under various circumstances. We show that in these cases, (approximate) values of the MLS on a sufficiently large finite set approximately determine the metric. Our approach is to recover the hypotheses of our main theorems in arXiv:2203.12128, namely multiplicative closeness of the MLS functions on the entire set of closed geodesics of $M$. We use mainly dynamical tools and arguments, but take great care to show the constants involved depend only on concrete geometric information about the given Riemannian metrics, such as the dimension, sectional curvature bounds, and injectivity radii. Comment: 22 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.15101 Zobrazit plný text záznamu View this record from Arxiv