Harmonic Analysis and Differential Equations Student Seminar: Geodesic stretch, pressure metric and the marked length spectrum rigidity conjecture

Seminar | November 12 | 3:40-5 p.m. | 740 Evans Hall

 Thibault Lefebvre, Paris 11

 Department of Mathematics

In 1985, Burns and Katok conjectured that the marked length spectrum of a negatively-curved Riemannian manifold (namely the collection of lengths of closed geodesics marked by the free homotopy of the manifold) should determine the metric up to isometries. This conjecture was independently proved for surfaces in 1990 by Croke and Otal but since then little progress has been accomplished in higher dimensions until our recent proof of the local version of the conjecture, obtained in collaboration with C. Guillarmou. Considering a geometric point of view in the moduli space of isometry classes, I will explain a new proof of this local version of the conjecture which relies on the notion of geodesic stretch. If time permits, I will show that this fits into a more general framework which generalizes Thurston’s distance and the pressure metric (initially defined on Teichmuller space) to the setting of variable curvature and higher dimensions. Joint work with C. Guillarmou, G. Knieper