Publications

2005

• On the null-controllability of the heat equation in unbounded domains
  
  • Miller Luc
  Bulletin des Sciences Mathématiques, Elsevier, 2005, 129 (2), pp.175-185. We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting)which implies that one can not go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the control region is bounded. The proof builds on heat kernel estimates. Secondly, we describe a class of null-controllable heat equations on unbounded product domains. Elementary examples include an infinite strip in the plane controlled from one boundary and an infinite rod controlled from an internal infinite rod. The proof combines earlier results on compact manifolds with a new lemma saying that the null-controllability of an abstract control system and its null-controllability cost are not changed by taking its tensor product with a system generated by a non-positive self-adjoint operator. (10.1016/j.bulsci.2004.04.003)
  DOI : 10.1016/j.bulsci.2004.04.003
• Convergence of weak solutions for the primitive system of the quasigeostrophic equations
  
  • Charve Frédéric
  Asymptotic Analysis, IOS Press, 2005, 452, pp.173-209.
• Stark-Wannier type operators with purely singular spectrum
  
  • Perelman Galina
  Asymptotic Analysis, IOS Press, 2005, 44, pp.1-45. We consider the one-dimensional Stark-Wannier type operators with potentials given by a smooth function with a logarithmic growth at infinity plus a periodic function with the Fourier coefficients of the form $(\ln |n|)^{-b}, 0
• 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.
• 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.
• 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.
• 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
• 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.