Quantitative marked length spectrum rigidity for surfaces
Abstract
We consider a closed negatively curved surface (M, g) with marked length spectrum sufficiently close (multiplicatively) to that of a hyperbolic metric g0 on M. We show there is a smooth diffeomorphism F:M M with derivative bounds close to 1, depending on the ratio of the two marked length spectrum functions. This is a two-dimensional version of our main result in [But25b].
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