Oka' s inequality for currents and applications.
Without relying on the classification of compact complex surfaces, it is proved that every such surface with even first Betti number admits a Kähler metric and that a real form of the classical Nakai-Moishezon criterion holds on the surface.
Let be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.