https://neckpinch.com/authors/daniel-mitsutani/New arXiv papers by Daniel Mitsutani, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2504.07290/arxiv: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