Prolongement d’applications holomorphes

Abstract

In this thesis, we will approach the subject of extension of holomorphic maps defined on the Hartogs open set taking values in complex. We start with the definition of the open set of Hartogs, and the theorem of Hartogs. We arrive at a definition for holomorphically extensifer (meromorphically extensifer) manifolds.

Then we give some known results and examples of holomorphically extensifer manifolds, for example a Hopf manifolds and almost homogeneous surfaces.

We conclude the thesis by addressing the question of the extension of holomorphic maps with values in elliptical surfaces, after we generalize this result to manifolds verifying some assumptions.