A -theory for the blow-up of second order elliptic equations of critical Sobolev growth.
A compactness result for polyharmonic maps in the critical dimension
For , let be a bounded smooth domain and a compact smooth Riemannian manifold without boundary. Suppose that is a sequence of weak solutions in the critical dimension to the perturbed -polyharmonic maps with in and weakly in . Then is an -polyharmonic map. In particular, the space of -polyharmonic maps is sequentially compact for the weak- topology.
A complement to the Fredholm theory of elliptic systems on bounded domains.
A discreteness criterion for the spectrum of the Laplace--Beltrami operator on quasimodel manifolds.
A few symmetry results for nonlinear elliptic PDE on noncompact manifolds
A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations
A geometric and analytic approach to some problems associated with Emden equations
A Lie transformation group attached to a second order elliptic operator.
A property of Sobolev spaces on complete Riemannian manifolds.
A reduction method for proving the existence of solutions to elliptic equations involving the -Laplacian.
A relationship between volume, injectivity radius, and eigenvalues.
A strong maximum principle for the Paneitz operator and a non-local flow for the -curvature
In this paper we consider Riemannian manifolds of dimension , with semi-positive -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive -curvature. Modifying the test function construction of Esposito-Robert, we show...
Almost product structures and Monge-Ampère equations.
Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds
In this paper, we consider elliptic differential operators on compact manifolds with a random perturbation in the 0th order term and show under fairly weak additional assumptions that the large eigenvalues almost surely distribute according to the Weyl law, well-known in the self-adjoint case.
An upper bound for the first eigenvalue of the Dirac operator on compact spin manifolds.
Analyse précisée d'équations semi-linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme
Analyse sur les boules d' un opérateur sous-elliptique.
Analytic index formulas for elliptic corner operators
Spaces with corner singularities, locally modelled by cones with base spaces having conical singularities, belong to the hierarchy of (pseudo-) manifolds with piecewise smooth geometry. We consider a typical case of a manifold with corners, the so-called "edged spindle", and a natural algebra of pseudodifferential operators on it with special degeneracy in the symbols, the "corner algebra". There are three levels of principal symbols in the corner algebra, namely the interior,...
Boundary value problems and layer potentials on manifolds with cylindrical ends
We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the...
Coherent orientations for periodic orbit problems in symplectic geometry.