Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Twisted constant scalar curvature Kähler metrics and Chen's continuity method

Yoshinori Hashimoto

created by daniele on 05 Apr 2018
modified on 09 Apr 2018

18 apr 2018 -- 14:30

Aula Tricerri, DiMaI, Firenze

Abstract.

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.

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