5 papers · 1 filter
The Pestov identity on the frame bundle and associated homogeneous fibrations
Mihajlo Cekić, 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.…
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 hom…
Local rigidity of manifolds with hyperbolic cusps I. Linear theory and microlocal tools
Yannick Guedes Bonthonneau, Thibault Lefeuvre
This paper is the first in a series of two articles whose aim is to extend a recent result of Guillarmou-Lefeuvre on the local rigidity of the marked length spectrum from the case…
The marked length spectrum of Anosov manifolds
Colin Guillarmou, Thibault Lefeuvre
In all dimensions, we prove that the marked length spectrum of a Riemannian manifold with Anosov geodesic flow and non-positive curvature locally determines the metric in t…
Boundary rigidity of negatively-curved asymptotically hyperbolic surfaces
Thibault Lefeuvre
In the spirit of Otal and Croke, we prove that a negatively-curved asymptotically hyperbolic surface is boundary distance rigid, where the distance between two points on the bounda…