15 citations · 58 across the 29 of their papers we have counts for
35 papers
On the singular set of the geodesic flow on nonpositively curved surfaces
Thibault Lefeuvre
We prove that the singular locus of the geodesic flow on the unit tangent bundle of a nonpositively curved surface enjoys an additional regularity property: its characteristic func…
Stability and uniqueness of minimal disks in non-constant curvature
Sébastien Alvarez, Thibault Lefeuvre, Ben Lowe +1
Nitsche proved that every smooth Jordan curve in of total curvature at most bounds a unique minimal disk, which is moreover strictly stable. We prove an analogu…
Foliated Plateau problems, surface Radon transforms, and boundary area rigidity in dimension three
Sébastien Alvarez, Thibault Lefeuvre, Ben Lowe +1
The present paper studies integral geometry problems on three-dimensional Riemannian balls, where integration is performed over minimal surfaces or, more generally, -surfaces de…
The spectrum of Anosov representations
Yannick Guedes Bonthonneau, Thibault Lefeuvre, Tobias Weich
Given a -Anosov representation into a noncompact semisimple real algebraic group , where is a parabolic subgroup, we construct a natural resonance spectrum for the cl…
Zonal states and improved bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces
Ambre Chabert, Thibault Lefeuvre
We establish polynomially improved bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces in the critical energy regime. We also show that, below the cr…
Propagation of regularity along unstable manifolds
Thibault Lefeuvre, Rafael Potrie
Let be a flow on a smooth closed connected manifold that preserves and expands a foliation . We establish a theorem of propagation of regularity along the le…
Semiclassical analysis of the magnetic Laplacian on hyperbolic surfaces
Thibault Lefeuvre
The magnetic Laplacian on hyperbolic surfaces provides a rich analytic framework in which a variety of quantum phenomena emerge. The present note, written for the \emph{Proceedings…
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 Poincar{é} rigidity near hyperbolic metrics
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 Poincar{é} determinant (MPD), a h…
Semiclassical defect measures of magnetic Laplacians on hyperbolic surfaces
Laurent Charles, Thibault Lefeuvre
On a closed hyperbolic surface, we investigate semiclassical defect measures associated with the magnetic Laplacian in the presence of a constant magnetic field. Depending on the e…
Semiclassical analysis on principal bundles
Mihajlo Cekić, Thibault Lefeuvre
Let be a compact Lie group. We introduce a semiclassical framework, called Borel-Weil calculus, to investigate -equivariant (pseudo)differential operators acting on -prin…
Correspondence between Pestov and Weitzenböck identities
Mihajlo Cekić, Thibault Lefeuvre, Andrei Moroianu +1
The aim of this note is to establish the correspondence between the twisted localized Pestov identity on the unit tangent bundle of a Riemannian manifold and the Weitzenböck identi…
Marked boundary rigidity for surfaces of Anosov type
Alena Erchenko, Thibault Lefeuvre
Let be a smooth compact connected oriented surface with boundary. A metric on is said to be of Anosov type if it has strictly convex boundary, no conjugate points, and a hy…
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 i…
Stability estimates for the Holonomy Inverse Problem
Mihajlo Cekić, Thibault Lefeuvre
On a Riemannian manifold with Anosov geodesic flow, the problem of recovering a connection from the knowledge of traces of its holonomies along primitive closed geodesics…
On the ergodicity of unitary frame flows on Kähler manifolds
Mihajlo Cekić, Thibault Lefeuvre, Andrei Moroianu +1
Let be a closed Kähler manifold with negative sectional curvature and complex dimension . In this article, we study the unitary frame flo…
Invariant distributions and the transport twistor space of closed surfaces
Jan Bohr, Thibault Lefeuvre, Gabriel P. Paternain
The purpose of this paper is to study transport equations on the unit tangent bundle of closed oriented Riemannian surfaces and to connect these to the transport twistor space of t…
Geodesic Lévy flights and expected stopping time for random searches
Yann Chaubet, Yannick Guedes Bonthonneau, Thibault Lefeuvre +1
We give an analytic description for the infinitesimal generator constructed by Applebaum-Estrade for Lévy flights on a broad class of closed Riemannian manifolds including all nega…
Isospectral connections, ergodicity of frame flows, and polynomial maps between spheres
Mihajlo Cekić, Thibault Lefeuvre
We show that on closed negatively curved Riemannian manifolds with simple length spectrum, the spectrum of the Bochner Laplacian determines both the isomorphism class of the vector…
Towards Brin's conjecture on frame flow ergodicity: new progress and perspectives
Mihajlo Cekić, Thibault Lefeuvre, Andrei Moroianu +1
We report on some recent progress achieved in [arXiv:2111.14811] on the ergodicity of the frame flow of negatively-curved Riemannian manifolds. We explain the new ideas leading to…
Local lens rigidity for manifolds of Anosov type
Mihajlo Cekić, Colin Guillarmou, Thibault Lefeuvre
The lens data of a Riemannian manifold with boundary is the collection of lengths of geodesics with endpoints on the boundary together with their incoming and outgoing vectors. We…
Isometric extensions of Anosov flows via microlocal analysis
Thibault Lefeuvre
We revisit the classical framework developed by Brin, Pesin and others to study ergodicity and mixing properties of isometric extensions of volume-preserving Anosov flows, using th…
On the ergodicity of the frame flow on even-dimensional manifolds
Mihajlo Cekić, Thibault Lefeuvre, Andrei Moroianu +1
It is known that the frame flow on a closed -dimensional Riemannian manifold with negative sectional curvature is ergodic if is odd and . In this paper we study it…
Generic injectivity of the X-ray transform
Mihajlo Cekić, Thibault Lefeuvre
In dimensions , we prove that the X-ray transform of symmetric tensors of arbitrary degree is generically injective with respect to the metric on closed Anosov manifolds an…