Publications

2005

• Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity
  
  • Rey Olivier
  • Wei Juncheng
  Journal of the European Mathematical Society, European Mathematical Society, 2005, 7, pp.449-476. We show that the critical nonlinear elliptic Neumann problem \[ \Delta u -\mu u + u^{7/3} = 0 \ \ \mbox{in} \ \Omega, \ \ u >0 \ \mbox{in} \ \Omega \ \mbox{and} \ \frac{ \partial u}{\partial \nu} = 0 \ \ \mbox{on} \ \partial \Omega\] where $\Omega$ is a bounded and smooth domain in $\mathbb{R}^5$, has arbitrarily many solutions, provided that $\mu>0$ is small enough. More precisely, for any positive integer $K$, there exists $\mu_K >0$ such that for $0 <\mu < \mu_K $, the above problem has a nontrivial solution which blows up at $K$ interior points in $\Omega$, as $\mu \to 0$. The location of the blow-up points is related to the domain geometry. The solutions are obtained as critical points of some finite dimensional reduced energy functional. No assumption on the symmetry, geometry nor topology of the domain is needed.
• Bergman kernels and symplectic reduction
  
  • Ma Xiaonan
  • Zhang Weiping
  Comptes rendus de l'Académie des sciences. Série I, Mathématique [1984-2001], Elsevier, 2005, 341, pp.pp. 297-302.
• Growth of discrete groups of isometries in negative curvature : a gap-property
  
  • Besson Gérard
  • Courtois Gilles
  • Gallot Sylvestre
  Comptes rendus de l'Académie des sciences. Série I, Mathématique [1984-2001], Elsevier, 2005, 341 (9), pp.567-572. (10.1016/j.crma.2005.09.025)
  DOI : 10.1016/j.crma.2005.09.025
• Killing forms on Quaternion-Kähler manifolds
  
  • Moroianu Andrei
  • Semmelmann Uwe
  Annals of Global Analysis and Geometry, Springer Verlag, 2005, 28, pp.319-335. We show that every Killing p-form on a compact quaternion-Kähler manifold has to be parallel for p greater than 1. (10.1007/s10455-005-1147-y)
  DOI : 10.1007/s10455-005-1147-y
• Polarizable twistor D-modules
  
  • Sabbah Claude
  , 2005, pp.208. We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, we construct a category of polarized twistor D-modules and show a Decomposition Theorem in this category.
• Kazhdan-Lusztig algorithms for nonlinear groups and applications to Kazhdan-Patterson lifting
  
  • Renard David
  American Journal of Mathematics, Johns Hopkins University Press, 2005, 127, pp.pp. 922-917.
• Hyperkaehler structures on the cotangent bundle of the restricted grassmannian and on a natural complexification of the restricted grassmannian
  
  • Tumpach Alice Barbara
  , 2005. In this paper, we describe an example of a hyperkaehler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can furthermore be identified either with the cotangent space of a connected component of the restricted grassmannian or with a natural complexification of this connected component, thus proving that these two manifolds are isomorphic hyperkaehler manifolds. In addition, Kaehler potentials are computed using Kostant-Souriau's theory of prequantization.
• Generalized cylinders in semi-Riemannian and spin geometry
  
  • Bär Christian
  • Gauduchon Paul
  • Moroianu Andrei
  Mathematische Zeitschrift, Springer, 2005, 249 (3), pp.545-580. We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into spaces of constant curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dirac operator. Moreover, we show that generalized Killing spinors for Codazzi tensors are restrictions of parallel spinors. Finally, we study the space of Lorentzian metrics and give a criterion when two Lorentzian metrics on a manifold can be joined in a natural manner by a 1-parameter family of such metrics. (10.1007/s00209-004-0718-0)
  DOI : 10.1007/s00209-004-0718-0
• Classification des variétés approximativement kähleriennes homogènes
  
  • Butruille Jean-Baptiste
  Annals of Global Analysis and Geometry, Springer Verlag, 2005, 27, pp.201-225. We prove Gray & Wolf's conjecture that a Riemannian homogeneous manifold admitting a strict nearly Kahler structure is 3-symmetric. We actually classify them in dimension 6 and use previous results of Swann, Cleyton and Nagy to prove the conjecture in higher dimensions.