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arXiv · 2609.29188

Local unmarked length spectrum rigidity for hyperbolic surfaces

Tristan Humbert
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Abstract

Let $(M,g)$ be a closed negatively curved surface. If $g$ is strictly $\tfrac 19$-pinched and has the same unmarked length spectrum as a hyperbolic metric, we show that $g$ is hyperbolic. As a consequence, we show that any hyperbolic metric on a surface admits a $C^2$-neighborhood in the space of metrics in which it is characterized by its unmarked length spectrum, up to isometry.

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Tristan Humbert. 2026-09-24. Local unmarked length spectrum rigidity for hyperbolic surfaces. https://arxiv.org/abs/2609.29188

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