The Poincaré-Lelong equation on complete Kähler manifolds
The positive mass theorem for ALE manifolds
We show what extra condition is necessary to be able to use the positive mass argument of Witten [12] on an asymptotically locally euclidean manifold. Specifically we show that the 'generalized positive action conjecture' holds if one assumes that the signature of the manifold has the correct value.
The Schrödinger equation on a compact manifold : Strichartz estimates and applications
We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any riemannian compact manifold. As a consequence we infer global existence results for the Cauchy problem of nonlinear Schrödinger equations on surfaces in the case of defocusing polynomial nonlinearities, and on three-manifolds in the case of quadratic nonlinearities. We also discuss the optimality of these Strichartz estimates on spheres.
The Srní lectures on non-integrable geometries with torsion
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...
Translation to bundle operators.
Ueber das Spektrum des Laplace-Operators auf kompakten Riemannschen Flächen.
Un principe de concentration-compacité pour les suites de surfaces Riemanniennes
Uniqueness of Harmonie Mappings and of Solutions of Elliptic Equations on Riemannnian Manifolds.
Universal prolongation of linear partial differential equations on filtered manifolds
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.
Valeurs propres immergées dans le spectre continu d'une surface de Riemann
Vanishing theorems for the basic cohomology of Riemannian foliations.
Variétés riemanniennes isométriques à l'infini.
Dans cet article, nous nous intéresserons à certaines propriétés des variétés riemanniennes non compactes qui ne dépendant que de leur géométrie à l'infini; pour cela, nous utiliserons un procédé de discrétisation qui associe un graph (pondéré) à une variété.
Weitzenböck Formula for SL(q)-foliations
A Weitzenböck formula for SL(q)-foliations is derived. Its linear part is a relative trace of the relative curvature operator acting on vector valued forms.
Zum Eigenwertverteilung invarianter elliptischer Operatoren.
Zur Abhängigkeit des Dirac-operators von der Spin-Struktur
Квазиклассическая асимптотика амплитуды рассеяния плоской волны на неоднородностях среды
Квантовая супералгебра osp(2/1)
О некоторых лиувиллевых теоремах на некомпактных римановых многообразиях
О нормальной разрешимости оператора внешнего дифференцирования на поверхности вращения.
Пример универсальной римановой поверхности, содержащей в качестве подобластей любые компактные поверхности с краем