14 citations · 23 across the 6 of their papers we have counts for
6 papers
Asymptotic regularity of sub-Riemannian eigenfunctions in dimension 3: the periodic case
Gabriel Rivière
On the unit tangent bundle of a compact Riemannian surface of constant nonzero curvature, we study semiclassical Schr{ö}dinger operators associated with the natural sub-Riemannian…
Length orthospectrum and the correlation function on flat tori
Nguyen Viet Dang, Matthieu Léautaud, Gabriel Rivière
This note presents some of the results obtained in arXiv:2207.05410 and it has beenthe object of a talk of the second author during the Journées "Équations auxDérivées Partielles"…
Long-time dynamics of the perturbed Schrödinger equation on negatively curved surfaces
Gabriel Riviere
We consider perturbations of the semiclassical Schr{ö}dinger equation on a compact Riemannian surface with constant negative curvature and without boundary. We show that, for scale…
norms, nodal sets, and quantum ergodicity
Hamid Hezari, Gabriel Riviere
For small range of , we improve the bounds of eigenfunctions of the Laplacian on negatively curved manifolds. Our improvement is by a power of logarithm for a full densi…
Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces
Suresh Eswarathasan, Gabriel Riviere
We consider the semiclassical Schrödinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, we look at…
Dispersion and controllability for the Schrödinger equation on negatively curved manifolds
Nalini Anantharaman, Gabriel Riviere
We study the time-dependent Schrödinger equation on a compact riemannian manifold on which the geodesic flow has the Anosov property.…