Yoshinori Hashimoto

The method of continuity has been successfully applied to solving many nonlinear PDE’s. A well-known example in complex geometry is the “Aubin continuity method” that is used to solve the Kähler-Einstein equation. An analogous continuity method was recently proposed by X.X. Chen, to find Kähler metrics of constant scalar curvature. In this talk we shall prove the openness in this continuity method of Chen - this amounts to finding “twisted constant scalar curvature Kähler metrics”, which is an interesting object in its own right. We shall also remark some algebro-geometric consequences of this result, and its potential relationship to the closedness of Chen’s continuity method.