Title: Horosphere boundary and extension of biholomorphisms

Abstract. This is a joint work with Filippo Bracci. Given a complete 
hyperbolic manifold (in the sense of Kobayashi), we consider an 
abstract boundary inspired by the one dimensional Caratheodory's  prime ends
theory. That boundary may be homeomorphic to the Euclidean boundary and to
the Gromov boundary (this is the case for strongly pseudoconvex domains in
the complex Euclidean space) or may be topologically different from these
two boundaries (this is the case for the bidisc). 
We use the construction of that boundary and results from the Gromov 
hyperbolicity theory to study continuous extension of biholomorphisms 
between certain non smooth domains.