Publications

1999

• On the normal bundle of minimal surfaces in almost Kahler 4-manifolds
  
  • Ville Marina
  , 1999.
• Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz
  
  • Moroianu Andrei
  Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 1999, 49, pp.1637-1659. Nous décrivons toutes les variétés kählériennes compactes de dimension complexe paire à courbure scalaire positive, admettant la plus petite valeur propre possible pour l'opérateur de Dirac.
• Generalized Killing Spinors and Conformal Eigenvalue Estimates for Spin^c Manifolds
  
  • Herzlich Marc
  • Moroianu Andrei
  Annals of Global Analysis and Geometry, Springer Verlag, 1999, 17, pp.341-370. In this paper we prove the Spin^c analog of the Hijazi inequality on the first eigenvalue of the Dirac operator on compact Riemannian manifolds and study its equality case. During this study, we are naturally led to consider generalized Killing spinors on Spin^c manifolds and we prove that such objects can only exist on low-dimensional manifolds (up to dimension three). This allows us to give a nice geometrical description of the manifolds satisfying the equality case of the above-mentioned inequality and to classify them in dimension three and four. (10.1023/A:1006546915261)
  DOI : 10.1023/A:1006546915261
• Harmonic metrics and connections with irregular singularities
  
  • Sabbah Claude
  Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 1999, 49 (4), pp.1265-1291. We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface X with the L^2 complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same L^2 complex. As a consequence, we obtain a Hard Lefschetz-type theorem.
• Special Spinors and Contact Geometry
  
  • Moroianu Andrei
  , 1999, pp.273-284. The aim of this note is to outline some new results obtained in contact geometry by means of spinorial methods and in particular to exhibit some interesting relations between (complex) contact structures and (Kaehlerian) Killing spinors.
• The topological impact of critical points at infinity in a variational problem with lack of compactness: the dimension 3
  
  • Rey Olivier
  Advances in Differential Equations, Khayyam Publishing, 1999, 4, pp.581-616. We extend to dimension 33 a result previously known in higher dimensions, concerning the topological effect of critical points at infinity on the level sets of a functional associated to an elliptic problem with critical nonlinearity.
• On the Kato inequality in Riemannian geometry
  
  • Herzlich Marc
  • Calderbank David M. J.
  • Gauduchon Paul
  , 2000, 4, pp.95-113.
• On a twisted de Rham complex
  
  • Sabbah Claude
  Tohoku mathematical journal, Mathematical Institute of Tohoku University, 1999, 51 (1), pp.125-140. We show that, given a projective regular function f on a smooth quasi-projective variety over C, the corresponding cohomology groups of the algebraic de Rham complex with twisted differential d-df and of the complex of algebraic forms with differential df have the same dimension (a result announced by Barannikov and Kontsevitch). We generalize the result to de Rham complexes with coefficients in a mixed Hodge Module. (10.2748/tmj/1178224856)
  DOI : 10.2748/tmj/1178224856
• An elliptic Neumann problem with critical nonlinearity in three dimensional domains
  
  • Rey Olivier
  Communications in Contemporary Mathematics, World Scientific Publishing, 1999, 1 (3), pp.405-449. We study an elliptic partial differential equation of second order with critical nonlinearity and Neumann boundary conditions. An improved asymptotic analysis allows us to prove in dimension 3 results previously known in larger dimensional spaces, i.e. existence and multiplicity of concentrated solutions in connection with properties of the mean curvature of the domain boundary.
• Semicontinuity of the spectrum at infinity
  
  • Nemethi Andras
  • Sabbah Claude
  Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Springer, 1999, 69 (1), pp.25-35. We prove that, for an analytic family of ''weakly tame'' regular functions on an affine manifold, the spectrum at infinity of each function of the family is semicontinuous in the sense of Varchenko. (10.1007/BF02940860)
  DOI : 10.1007/BF02940860
• Hypergeometric periods for a tame polynomial
  
  • Sabbah Claude
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 1999, 328 (7), pp.603-608. We analyse the Gauss-Manin system of differential equations---and its Fourier transform---attached to regular functions satisfying a tameness assupmption on a smooth affine variety over C (e.g. tame polynomials on C^{n+1}). We give a solution to the Birkhoff problem and prove Hodge-type results analogous to those existing for germs of isolated hypersurface singularities. (10.1016/S0764-4442(99)80254-7)
  DOI : 10.1016/S0764-4442(99)80254-7