5 papers
Monotonicity of the Liouville entropy along the Ricci flow on surfaces
Karen Butt, Alena Erchenko, Tristan Humbert +1
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 (NR…
Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces
Alena Erchenko, Dmitry Jakobson, Allison Tsypin
It is known that the small eigenvalues of the Laplacian of a Riemann surface close to the boundary of the modular space can be well approximated by the eigenvalues of the discrete…
Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3
Alena Erchenko, Kurt Vinhage, Yun Yang
In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of th…
Marked Poincaré rigidity near hyperbolic metrics and injectivity of the Lichnerowicz Laplacian in dimension 3
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 Poincaré determinant (MPD), a ho…
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…