18 apr 2018 -- 14:30
Aula Tricerri, DiMaI, Firenze
With the aim of finding a constant scalar curvature Kähler metric on a compact Kähler manifold, X.X. Chen recently proposed a continuity method that is analogous to Aubin's continuity method for Kähler--Einstein metrics. An interesting feature of this continuity method is that the order of PDE "jumps" at the initial point t=0, and that the intermediate metric at 0<t<1 is an object called twisted constant scalar curvature Kähler metrics. In this talk we shall prove the openness of this continuity method; this amounts to proving the existence of certain twisted constant scalar curvature Kähler metrics, which is of interest in its own right.