Elliptic operators and covers of Riemannian manifolds.
Elliptic operators and higher signatures
Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov’s higher signatures on closed manifolds, - the problem of cut-and-paste invariance of Novikov’s higher signatures on closed manifolds, - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.
Ellipticity of the symplectic twistor complex
For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the symplectic...
Equations de Fokker-Planck géométriques II : estimations hypoelliptiques maximales
Nous donnons des résultats analytiques sur les propriétés de régularité du laplacien hypoelliptique de Jean-Michel Bismut et plus généralement sur les opérateurs de type Fokker-Planck géométrique agissant sur le fibré cotangent d’une variété riemannienne compacte . En particulier, nous prouvons un résultat d’hypoellipticité maximale pour , et nous en déduisons des bornes sur la localisation de ses valeurs spectrales.
Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists...
Existence and uniqueness of classical solutions to second-order quasilinear elliptic equations.
Exotic solutions of the conformal scalar curvature equation in Rn
Exponential coordinates and regularity of groupoid heat kernels
We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.