-preserving Schrödinger heat flow under the Ricci flow.
pinching and compactness theorems for compact riemannian manifolds
La -aire selon M. Gromov
Le problème de Yamabe sur des sous domaines de
Le spectre du laplacien agissant sur les formes différentielles
Level sets of Gauss curvature in surfaces of constant mean curvature
Line vortices in the U(1) Higgs model
L'inégalité de Penrose
Lines vortices in the U(1) - Higgs model
For a given U(1)-bundle E over M = {x1, ..., xn}, where the xi are n distinct points of , we minimise the U(1)-Higgs action and we make an asymptotic analysis of the minimizers when the coupling constant tends to infinity. We prove that the curvature (= magnetic field) converges to a limiting curvature that we give explicitely and which is singular along line vortices which connect the xi. This work is the three dimensional equivalent of previous works in dimension two (see [3] and [4]). The...
Liouville theorem for harmonic maps with potential.
Local gradient estimates of -harmonic functions, -flow, and an entropy formula
In the first part of this paper, we prove local interior and boundary gradient estimates for -harmonic functions on general Riemannian manifolds. With these estimates, following the strategy in recent work of R. Moser, we prove an existence theorem for weak solutions to the level set formulation of the (inverse mean curvature) flow for hypersurfaces in ambient manifolds satisfying a sharp volume growth assumption. In the second part of this paper, we consider two parabolic analogues of the -harmonic...
Lp-pinching and the geometry of compact Riemannian manifolds.