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arXiv · 2509.16829

Quantitative marked length spectrum rigidity for surfaces

Karen Butt
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Abstract

We consider a closed negatively curved surface $(M, g)$ with marked length spectrum sufficiently close (multiplicatively) to that of a hyperbolic metric $g_0$ on $M$. We show there is a smooth diffeomorphism $F:M \to M$ 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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Karen Butt. 2025-09-20. Quantitative marked length spectrum rigidity for surfaces. https://arxiv.org/abs/2509.16829

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