https://neckpinch.com/authors/karen-butt/New arXiv papers by Karen Butt, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.36354arxiv:2610.36354Mon, 26 Oct 2026 00:00:00 GMTKaren Butt, Alena Erchenko, Tristan Humbert — For closed negatively curved surfaces, we obtain formulas for the derivatives of the harmonic entropy of its geodesic flow and the linear drift of its Brownian motion along conformal deformations. We deduce that the harmonic entropy of the geodesic flow of a closed surface of non-constant negative curvature (resp. linear drift of the Brownian motion on its universal cover) is strictly decreasing (resp. increasing) along the normalized Ricci flow. We also prove that any hyperbolic metric on a surface admits a neighborhood in the space of conformal negatively curved metrics in which the linear drift is greater or equal to the Liouville entropy, with equality if and only if the metric is hyperbolic.Ricci flowSurfaces https://arxiv.org/abs/2511.06137arxiv:2511.06137Sat, 08 Nov 2025 00:00:00 GMTKaren Butt, Alena Erchenko, Tristan Humbert — 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.Ricci flow https://arxiv.org/abs/2504.07290arxiv:2504.07290Wed, 09 Apr 2025 00:00:00 GMTKaren Butt, Alena Erchenko, Tristan Humbert, Daniel Mitsutani — We show that the Liouville entropy of the geodesic flow of a closed surface of non-constant negative curvature is eventually strictly increasing along the normalized Ricci flow (NRF). More precisely, we obtain a new expression for the derivative of the Liouville entropy along an arbitrary conformal deformation in dimension 2, and we prove it is positive in the direction of the NRF for 1/6-pinched metrics. This partially answers a question of Manning from 2004. In addition, we show that the mean root curvature, a purely geometric quantity which is a lower bound for the Liouville entropy, is strictly increasing along the NRF starting from any metric of non-constant negative curvature.Ricci flowSurfaces