Canonical metrics on some domains of
The study of the existence and uniqueness of a preferred Kähler metric on a given complex manifold is a very important area of research. In this talk we recall the main results and open questions for the most important canonical metrics (Einstein, constant scalar curvature, extremal, Kähler-Ricci solitons) in the compact and the non-compact case, then we consider a particular class of complex domains in , the so-called Hartogs domains, which can be equipped with a natural Kaehler metric ....