L2 estimates and existence theorems for the tangential Cauchy-Riemann complex.
Soit un fibré holomorphe localement trivial de base une variété de Stein et de fibre une courbe compacte.Si est un ouvert localement pseudoconvexe de ne contenant aucune fibre, alors est de Stein.
Let G be a complex semi-simple group with a compact maximal group K and an irreducible holomorphic representation ρ on a finite dimensional space V. There exists on V a K-invariant Hermitian scalar product. Let Ω be the intersection of the unit ball of V with the G-orbit of a dominant vector. Ω is a generalization of the unit ball (case obtained for G = SL(n,C) and ρ the natural representation on Cn).We prove that for such manifolds, the Bergman and Szegö kernels as for the ball are rational fractions...
We give a sufficient condition for a (resp. )-totally real, complex-tangential, -dimensional submanifold in a weakly pseudoconvex boundary of class (resp. ) to be a local peak set for the class (resp. ). Moreover, we give a consequence of it for Catlin’s multitype.