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arXiv · 2509.00188

On the stability of Ricci flow on hyperbolic 3-manifolds of finite volume

Ruojing Jiang·Franco Vargas Pallete
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Abstract

On a hyperbolic 3-manifold of finite volume, we prove that if the initial metric is sufficiently close to the hyperbolic metric $h_0$, then the normalized Ricci-DeTurck flow exists for all time and converges exponentially fast to $h_0$ in a weighted H\"older norm. A key ingredient of our approach is the application of interpolation theory. Furthermore, this result is a valuable tool for investigating minimal surface entropy, which quantifies the growth rate of the number of closed minimal surfaces in terms of genus. We explore this in [17].

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Ruojing Jiang, Franco Vargas Pallete. 2025-08-29. On the stability of Ricci flow on hyperbolic 3-manifolds of finite volume. https://arxiv.org/abs/2509.00188

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