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math.DG2025
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…
math.DG2025
The Pestov identity on the frame bundle and associated homogeneous fibrations
Mihajlo CekiÄ, Thibault Lefeuvre, Andrei Moroianu +1
In this short note, we prove a global Pestov identity on the (orthonormal) frame bundle of a Riemannian manifold and deduce similar identities on associated homogeneous fibrations.…
math.DG2024
Marked length spectrum rigidity for Anosov surfaces
Colin Guillarmou, Thibault Lefeuvre, Gabriel P. Paternain
Let be a smooth closed oriented surface of genus . We prove that two metrics on with the same marked length spectrum and Anosov geodesic flow are isometric via an…