Publications

2005

• 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.
• 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
• 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.
• 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
• Stability of the absolutely continuous spectrum for multi-dimensional Schrödinger operators
  
  • Perelman Galina
  International Mathematics Research Notices, Oxford University Press (OUP), 2005, 2005, pp.37, pp. 2289.
• Sommes de carrés de fonctions dérivables
  
  • Bony Jean-Michel
  Bulletin de la société mathématique de France, Société Mathématique de France, 2005, 133, pp.fas. 4.
• Elliptic genus and vertex operator algebras
  
  • Ma Xiaonan
  • Dong Chongying
  • Liu Kefeng
  Quarterly journal of pure and applied mathematics, 2005, 1- 2005, pp.791-815.
• Unique continuation estimates for the Laplacian and the heat equation on non-compact manifolds
  
  • Miller Luc
  Mathematical Research Letters, International Press, 2005, 12 (1), pp.37-47. This article concerns some quantitative versions of unique continuation known as observability inequalities. One of them is a lower bound on the spectral projectors of the Dirichlet Laplacian which generalizes the unique continuation of an eigenfunction from any open set Omega. Another one is equivalent to the interior null-controllability in time T of the heat equation with Dirichlet condition (the input function is a source in (0,T) x Omega). On a compact Riemannian manifolds, these inequalities are known to hold for arbitrary T and Omega. This article states and links these observability inequalities on a complete non-compact Riemannian manifold, and tackles the quite open problem of finding which Omega and T ensure their validity. It proves that it is sufficient for Omega to be the exterior of a compact set (for arbitrary T), but also illustrates that this is not necessary. It provides a necessary condition saying that there is no sequence of balls going infinitely far "away" from Omega without "shrinking" in a generalized sense (depending on T) which also applies when the distance to Omega is bounded.
• Controllability cost of conservative systems: resolvent condition and transmutation
  
  • Miller Luc
  Journal of Functional Analysis, Elsevier, 2005, 218 (2), pp.425-444. This article concerns the exact controllability of unitary groups on Hilbert spaces with unbounded control operator. It provides a necessary and sufficient condition not involving time which blends a resolvent estimate and an observability inequality. By the transmutation of controls in some time L for the corresponding second order conservative system, it is proved that the cost of controls in time T for the unitary group grows at most like \exp(\alpha L^{2}/T) as T tends to 0. In the application to the cost of fast controls for the Schrödinger equation, L is the length of the longest ray of geometric optics which does not intersect the control region. This article also provides observability resolvent estimates implying fast smoothing effect controllability at low cost, and underscores that the controllability cost of a system is not changed by taking its tensor product with a conservative system. (10.1016/j.jfa.2004.02.001)
  DOI : 10.1016/j.jfa.2004.02.001