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math.DG2025
Monotonicity of topological entropy along the Ricci flow near a hyperbolic metric
Karen 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 f…
math.DG2025
Marked Poincar{é} rigidity near hyperbolic metrics
Karen Butt, Alena Erchenko, Tristan Humbert +2
Let be a compact manifold without boundary equipped with a Riemannian metric of negative curvature. In this paper, we introduce the marked Poincar{é} determinant (MPD), a h…