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arXiv · 2511.06137

Monotonicity of topological entropy along the Ricci flow near a hyperbolic metric

Karen Butt·Alena Erchenko·Tristan Humbert
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Abstract

In 2004, Manning showed that the topological entropy of the geodesic flow of a closed surface of non-constant negative curvature is strictly decreasing along the normalized Ricci flow, and he asked if an analogous result holds in higher dimensions for metrics in a neighborhood of a hyperbolic metric. In this paper, we affirmatively answer this question. Namely, we show that the topological entropy of the geodesic flow of a closed Riemannian manifold that carries a hyperbolic metric is indeed strictly decreasing along the normalized Ricci flow starting from a metric of variable negative sectional curvature sufficiently close to the hyperbolic metric.

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Karen Butt, Alena Erchenko, Tristan Humbert. 2025-11-08. Monotonicity of topological entropy along the Ricci flow near a hyperbolic metric. https://arxiv.org/abs/2511.06137

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