L2 methods in complex analysis

Abstract

The main goal of this expository thesis is to study the L2-technique of Hörmander estimates. Beginning with some elementary considerations, such as Poincaré’s theorem, domains of holomorphy and the Hartogs theorem, we deal with two interesting applications: 1) An elegant solution to the celebrated Levi problem 2) Holomorphic extensions in the sense of Ohsawa-Takegoshi We conclude the thesis by discussing the corresponding analogue of the Hörmander’s estimate on compact Kähler manifolds.