Some differential operators connected with quasiconformal deformations on manifold
Some existence results for the scalar curvature problem via Morse theory
We prove existence of positive solutions for the equation on , arising in the prescribed scalar curvature problem. is the Laplace-Beltrami operator on , is the critical Sobolev exponent, and is a small parameter. The problem can be reduced to a finite dimensional study which is performed with Morse theory.
Some new conformal covariants.
Some progress in conformal geometry.
Some regularity theorems in riemannian geometry
Spectral Geometry for Certain Noncompact Riemannian Manifolds.
Spectrum and Holonomy of the Line Bundle over the Sphere.
Spectrum of a compact flat manifold.
Sur la mulitplicité de la première valeur propre non nulle du Laplacien.
Surfaces in three-dimensional Lie groups.
Symétrisation d'inéquations élliptiques et applications géométriques.
Symplectic Killing spinors
Let be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection . Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main object of this paper. We derive a necessary condition which has to be satisfied by a symplectic Killing spinor field. Using this condition one may easily...
Symplectic spinor valued forms and invariant operators acting between them
Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.
The almost Einstein operator for distributions
For the geometry of oriented distributions , which correspond to regular, normal parabolic geometries of type for a particular parabolic subgroup , we develop the corresponding tractor calculus and use it to analyze the first BGG operator associated to the -dimensional irreducible representation of . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions of this operator...
The Cauchy problem for Lorentz metrics with prescribed Ricci curvature
The CR Yamabe conjecture the case
Let be a compact CR manifold of dimension with a contact form , and its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form on conformal to which has a constant Webster curvature. This problem is equivalent to the existence of a function such that , on . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where and is not locally CR equivalent to the sphere of . In a join work with R. Yacoub, the CR Yamabe problem...
The First Eigenvalue of the Laplacian of an Isoparametric Minimal Hypersurface in a Unit Sphere.
The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds
The heat semigroup acting on tensors or differential forms with values in vector bundle
The Paneitz equation in hyperbolic space