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- W4307535295 abstract "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." @default.
- W4307535295 created "2022-11-03" @default.
- W4307535295 creator A5078229466 @default.
- W4307535295 date "2022-10-26" @default.
- W4307535295 modified "2023-09-26" @default.
- W4307535295 title "Approximate control of the marked length spectrum by short geodesics" @default.
- W4307535295 doi "https://doi.org/10.48550/arxiv.2210.15101" @default.
- W4307535295 hasPublicationYear "2022" @default.
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