38 citations · 193 across the 31 of their papers we have counts for
32 papers
Quantum Limits on product manifolds
Emmanuel Humbert, Yannick Privat, Emmanuel Trélat
We establish some properties of quantum limits on a product manifold, proving for instance that, under appropriate assumptions, the quantum limits on the product of manifolds are a…
Observability for generalized Schrödinger equations and quantum limits on product manifolds
Emmanuel Humbert, Yannick Privat, Emmanuel Trélat
Given a closed product Riemannian manifold N = M x M equipped with the product Riemannian metric g = h + h , we explore the observability properties for the generalized Schr{ö}ding…
Geometric and spectral characterization of Zoll manifolds, invariant measures and quantum limits
Emmanuel Humbert, Yannick Privat, Emmanuel Trélat
We provide new geometric and spectral characterizations for a Riemannian manifold to be a Zoll manifold, i.e., all geodesics of which are periodic. We analyze relationships with in…
Mass functions of a compact manifold
Andreas Hermann, Emmanuel Humbert
Let be a compact manifold of dimension . In this paper, we introduce the {\em Mass Function} $a \geq 0 \mapsto \xp{M}{a}$ (resp. $a \geq 0 \mapsto \xm{M}{a}$) which is defin…
Observability properties of the homogeneous wave equation on a closed manifold
Emmanuel Humbert, Yannick Privat, Emmanuel Trélat
We consider the wave equation on a closed Riemannian manifold. We observe the restriction of the solutions to a measurable subset along a time interval with . It…
Optimal transportation between hypersurfaces bounding some strictly convex domains
Emmanuel Humbert, Luc Molinet
Let be two smooth compact hypersurfaces of which bound strictly convex domains equipped with two absolutely continuous measures and (with respect to th…