On the Paneitz energy on standard three sphere
We prove that the Paneitz energy on the standard three-sphere S3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
On the Sobolev constant and the -spectrum of a compact riemannian manifold
On the Spectrum of Non-Compact Manifolds with Finite Volume.
Opérateurs transversalement elliptiques sur un feuilletage riemannien et applications
Persistence of invariant manifolds for perturbations of semiflows with symmetry.
Prescribing -curvature on higher dimensional spheres
We study the problem of prescribing a fourth order conformal invariant on higher dimensional spheres. Particular attention is paid to the blow-up points, i.e. the critical points at infinity of the corresponding variational problem. Using topological tools and a careful analysis of the gradient flow lines in the neighborhood of such critical points at infinity, we prove some existence results.
Regularity Theorems in Riemannian Geometry. II. Harmonic Curvature and the Weyl Tensor.
Relationship between Laplacian operator and D'Alembertian operator.
Remarques sur la conjecture de Weyl
Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces
Any Kähler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dimension.
Rigidity of generalized laplacians and some geometric applications. (Summary).
Rigidity of generalized laplacians and some geometric applications.
Semigroup properties for the second fundamental form.
Semiholonomic jets and induced modules in Cartan geometry calculus
The famous Erlangen Programme was coined by Felix Klein in 1872 as an algebraic approach allowing to incorporate fixed symmetry groups as the core ingredient for geometric analysis, seeing the chosen symmetries as intrinsic invariance of all objects and tools. This idea was broadened essentially by Elie Cartan in the beginning of the last century, and we may consider (curved) geometries as modelled over certain (flat) Klein’s models. The aim of this short survey is to explain carefully the basic...
Separable -harmonic functions in a cone and related quasilinear equations on manifolds
Sharp borderline Sobolev inequalities on compact Riemannian manifolds.
Sharp Inequalities and Geometric Manifolds.
Sobolev-Kantorovich Inequalities
In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means...
Solution explicite de l'équation des ondes dans un espace symétrique de type non compact de rang 1
Solving -Laplacian equations on complete manifolds.