Geodesic stretch, pressure metric and marked length spectrum rigidity
Differential Geometry
2023-06-22 v2 Analysis of PDEs
Dynamical Systems
Abstract
We refine the recent local rigidity result for the marked length spectrum obtained by the first and third author in \cite{Guillarmou-Lefeuvre-18} and give an alternative proof using the geodesic stretch between two Anosov flows and some uniform estimate on the variance appearing in the central limit theorem for Anosov geodesic flows. In turn, we also introduce a new pressure metric on the space of isometry classes, that reduces to the Weil-Peterson metric in the case of Teichm\"uller space and is related to the works of \cite{McMullen,Bridgeman-Canary-Labourie-Sambarino-15}.
Keywords
Cite
@article{arxiv.1909.08666,
title = {Geodesic stretch, pressure metric and marked length spectrum rigidity},
author = {Colin Guillarmou and Gerhard Knieper and Thibault Lefeuvre},
journal= {arXiv preprint arXiv:1909.08666},
year = {2023}
}
Comments
47 pages, corrections and additions of material after refereeing process