Local holomorphic extension of CR-functions -

Abstract

This thesis involves the extension behavior of holomorphic functions in several variables, and the corresponding extension problem for CR functions defined on a real hypersurface of a complex manifold. However, the extension behavior of a holomorphic function f defined on a domain U turns out to depend on the complex geometry of the boundary bU of U: thus the problem can be often formulated in terms of the trace of f on U rather than f itself. Then what follows is the notion of CR functions: complex-valued functions defined on real submanifolds of Cn. Specifically we will discuss some important extension results for CR functions, with particular emphasis on H.Lewy’s classical result about the extension from strictly pseudoconvex hypersurfaces.