Geodesic stretch, pressure metric and marked length spectrum rigidity
arXiv:1909.08666 · doi:10.1017/etds.2021.75
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 Teichmüller space and is related to the works of \cite{McMullen,Bridgeman-Canary-Labourie-Sambarino-15}.
47 pages, corrections and additions of material after refereeing process
References in corpus (6)
- Minimal stretch maps between hyperbolic surfaces
- Upper bound on the density of Ruelle resonances for Anosov flows
- Invariant distributions and X-ray transform for Anosov flows
- Fried conjecture in small dimensions
- Classical and microlocal analysis of the X-ray transform on Anosov manifolds
- Regularity of entropy, geodesic currents and entropy at infinity