Global solution of the wave equation
Harmonic diffeomorphisms and Teichmüller theory.
Harmonic Differential Operators.
Harmonic symplectic spinors on Riemann surfaces.
Harnack inequalities on a manifold with positive or negative Ricci curvature.
Several new Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive (or a negative) constant are established. These estimates are sharp both for small time, for large time and for large distance, and lead to new estimates for the heat kernel of a manifold with Ricci curvature bounded below.
Heat kernel estimates and lower bound of eigenvalues.
Hyper-differential operators in complex space
Injectivity radius and low eigenvalues of hyperbolic manifolds.
Integrable systems and projective images of Kummer surfaces
Invariants intégraux fonctionnels pour des équations aux dérivées partielles d'origine géométrique
Kähler-Einstein metrics singular along a smooth divisor
In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor . We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical or edge...
-boundedness of oscillating spectral multipliers on Riemannian manifolds
We prove endpoint estimates for operators given by oscillating spectral multipliers on Riemannian manifolds with -bounded geometry and nonnegative Ricci curvature.
pinching and compactness theorems for compact riemannian manifolds
Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein.
L'inégalité de Penrose
Liouville theorem for harmonic maps with potential.
Liouville type theorems for φ-subharmonic functions.
In this paper we present some Liouville type theorems for solutions of differential inequalities involving the φ-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the p-Laplacian, and are new even in these cases. Phragmen-Lindeloff type results, and a weak form of the Omori-Yau maximum principle are also discussed.
Mass endomorphism, surgery and perturbations
We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.
Maximale eindeutige Lösungen (Riemannsche Flächen) für Cauchysche Anfangswertaufgaben bei partiellen Differentialgleichungssystemen erster Ordnung für eine gesuchte Funktion auf C°°-Mannigfaltigkeiten I.
Maximale eindeutige Lösungen (Riemannsche Flächen) für Cauchysche Anfangswertaufgaben bei partiellen Differentialgleichungssystemen erster Ordnung für eine gesuchte Funktion auf C°°-Mannigfaltigkeiten. III.