Seminario Dottorato: Holomorphic sectors and boundary behavior of holomorphic functions

Wednesday 26 May 2010 - Raffaele Marigo

ARGOMENTI: Seminari Dottorato

SEMINARIO DOTTORATO
Wednesday 26 May 2010 h. 14:30, room 1BC/50
Raffaele Marigo (Univ. Padova - Dip. Mat.)
"Holomorphic sectors and boundary behavior of holomorphic functions"

-Abstract
Forced extendibility of holomorphic functions is one of the most important problems in several complex variables: it is a well known fact that a function defined in an open set D of C^n extends across the boundary at a point where the Levi form of the boundary of D (i.e. the complex hessian of its defining function restricted to the complex tangent space) has at least one negative eigenvalue. A fundamental role in this result is played by analytic discs, i.e. holomorphic images of the standard disc.
After describing the construction of discs attached to a hypersurface by solving a functional equation - Bishop equation - in the spaces of differentiable functions with fractional regularity, we will show how they induce the phenomenon described above, as well as the propagation of holomorphic extendibility along a disc tangent to the boundary of the domain. Finally, we will introduce a new family of discs, nonsmooth along the boundary, that will allow us to establish analogous results under various geometric conditions on the boundary of the domain.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva