Marked length spectrum, geodesic stretch and pressure metric

Abstract: The marked length spectrum of a negatively-curved manifold is the data of all the lengths of closed geodesics, marked by the free homotopy of the manifold. The marked length spectrum conjecture (also known as the Burns-Katok conjecture, 1985) asserts that two negatively-curved manifolds with same marked length spectrum should be isometric. This conjecture was proved on surfaces (Croke '90, Otal '90) but remains open in higher dimensions. I will present a proof of a local version of this conjecture, based on the notions of geodesic stretch and pressure metric (a generalization of the Weil-Petersson metric to the context of variable curvature). Some elements of the theory of Pollicott-Ruelle resonances and anisotropic spaces will also be needed (I will recall everything). Joint work with C. Guillarmou and G. Knieper.

differential geometry

Audience: researchers in the topic

Pangolin seminar

Series comments: TIME HAS CHANGED: 15:30 Paris 10:30AM Rio de Janeiro

Description: Differential geometry seminar

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