Publications

2009

• Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S^2
  
  • Figalli Alessio
  • Rifford Ludovic
  Communications on Pure and Applied Mathematics, Wiley, 2009, 62 (12), pp.1670-1706. (10.1002/cpa.20293)
  DOI : 10.1002/cpa.20293
• Addendum à l'article "Histoire d'un vecteur tricentenaire
  
  • Guichardet Alain
  Gazette des Mathématiciens, Société Mathématique de France, 2009, 119, pp.32.
• Maximal slope of tensor product of Hermitian vector bundles
  
  • Chen Huayi
  Journal of Algebraic Geometry, American Mathematical Society, 2009, 18 (3), pp.575-603. We give an upper bound for the maximal slope of the tensor product of several non-zero Hermitian vector bundles on the spectrum of an algebraic integer ring. By Minkowski's theorem, we need to estimate the Arakelov degree of an arbitrary Hermitian line subbundle $\overline M$ of the tensor product. In the case where the generic fiber of $M$ is semistable in the sense of geometric invariant theory, the estimation is established by constructing, through the classical invariant theory, a special polynomial which does not vanish on the generic fibre of $M$. Otherwise we use an explicte version of a result of Ramanan and Ramanathan to reduce the general case to the former one. (10.1090/S1056-3911-08-00513-4)
  DOI : 10.1090/S1056-3911-08-00513-4
• Cubic polynomials: a measurable view on parameter space
  
  • Dujardin Romain
  , 2009, pp.451-489. We study the fine geometric structure of bifurcation currents in the parameter space of cubic polynomials viewed as dynamical systems. In particular we prove that these currents have some laminar structure in a large region of parameter space, reflecting the possibility of quasiconformal deformations. On the other hand, there is a natural bifurcation measure, supported on the closure of rigid parameters. We prove a strong non laminarity statement relative to this measure. (10.1201/b10617-15)
  DOI : 10.1201/b10617-15
• A remark on soliton-potential interactions for nonlinear Schrödinger equations
  
  • Perelman Galina
  Math. Res. Lett., 2009, 16 (3), pp.477-486.. We exhibit a time reversible geometric flow of planar curves which can develop singularities in finite time within the uniform topology. The example is based on the construction of selfsimilar solutions of modified Korteweg-de Vries equation of a given (small) mean.