https://neckpinch.com/authors/franco-vargas-pallete/New arXiv papers by Franco Vargas Pallete, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2509.00197/arxiv:2509.00197Fri, 29 Aug 2025 00:00:00 GMTRuojing Jiang, Franco Vargas Pallete — This paper studies minimal surface entropy (the exponential asymptotic growth of the number of minimal surfaces up to a given value of area) for negatively curved metrics on hyperbolic 3-manifolds of finite volume, particularly its comparison to the hyperbolic minimal surface entropy in terms of sectional and scalar curvature. On one hand, for metrics that are bilipschitz equivalent to the hyperbolic metric and have sectional curvature bounded above by −1 and uniformly bounded below, we show that the entropy achieves its minimum if and only if the metric is hyperbolic. On the other hand, by analyzing the convergence rate of the Ricci flow toward the hyperbolic metric, we prove that among all metrics with scalar curvature bounded below by −6 and with non-positive sectional curvature on the cusps, the entropy is maximized at the hyperbolic metric, provided that it is infinitesimally rigid. Furthermore, if the metrics are uniformly C⁰-close to the hyperbolic metric and asymptotically cusped, then the entropy associated with the Lebesgue measure is uniquely maximized at the hyperbolic metric.Ricci flow3-manifoldsSphere theoremsScalar curvatureMinimal & CMC surfaces https://neckpinch.com/papers/2509.00188/arxiv:2509.00188Fri, 29 Aug 2025 00:00:00 GMTRuojing Jiang, Franco Vargas Pallete — On a hyperbolic 3-manifold of finite volume, we prove that if the initial metric is sufficiently close to the hyperbolic metric h₀, then the normalized Ricci-DeTurck flow exists for all time and converges exponentially fast to h₀ in a weighted Hölder 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].Ricci flow3-manifoldsStability & uniquenessLong-time existence & convergenceHarmonic maps & DeTurck trickMinimal & CMC surfaces