Bounded domains which are isospectral but not congruent
Branching of asymptotics for elliptic operators on manifolds with edges
Branson's -curvature in Riemannian and spin geometry.
Breaking of Symmetries for Forced Equations.
Brownian motion and random walks on manifolds
We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.
Brownian motion and stereographic projection
Brownian motion and transient groups
In this paper I consider a covering of a Riemannian manifold . I prove that Green’s function exists on if any and only if the symmetric translation invariant random walks on the covering group are transient (under the assumption that is compact).
Brownian motion, excursions, and matrix factors
Brownian motion on a surface of negative curvature
Brownian motion on compact manifolds: cover time and late points.
Brownian motion with respect to time-changing riemannian metrics, applications to Ricci flow
We generalize brownian motion on a riemannian manifold to the case of a family of metrics which depends on time. Such questions are natural for equations like the heat equation with respect to time dependent laplacians (inhomogeneous diffusions). In this paper we are in particular interested in the Ricci flow which provides an intrinsic family of time dependent metrics. We give a notion of parallel transport along this brownian motion, and establish a generalization of the Dohrn–Guerra or damped...
Brownian motions in the diffeomorphism group I
Bubbling along boundary geodesics near the second critical exponent
The role of the second critical exponent , the Sobolev critical exponent in one dimension less, is investigated for the classical Lane–Emden–Fowler problem , under zero Dirichlet boundary conditions, in a domain in with bounded, smooth boundary. Given , a geodesic of the boundary with negative inner normal curvature we find that for , there exists a solution such that converges weakly to a Dirac measure on as , provided that is nondegenerate in the sense of second variations of...
-symmetries and reduction of equations without Lie point symmetries.
Calcul des variations sur un brownien subordonné
Calcul du spectre de certaines nilvariétés compactes de dimension 3
Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. II
Soit un opérateur pseudodifférentiel (ou microdifférentiel) tel que soit aussi un opérateur pseudodifférentiel. Alors le symbole de s’ecrit avec un symbole . Pour la réciproque, si est un opérateur à symbole , il existe un opérateur tel que . Tous ces résultats reposent sur la théorie développée dans la Note I de cette série. Comme application, on obtient une condition suffisante d’inversibilité pour les opérateurs pseudodifférentiels d’ordre infini.
Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I
Cet article s’intéresse au calcul symbolique des opérateurs microdifférentiels avec symboles exponentiels. On donne la loi de composition des symboles exponentiels. Comme application, on trouve une condition suffisante d’ellipticité pour les opérateurs microdifférentiels d’ordre infini.
Calcul stochastique avec sauts sur une variété
Canonical lift and exit law of the fundamental diffusion associated with a kleinian group