EVENT DETAILS AND ABSTRACT

Title: Ricci flow and the completion of the space of Kahler metrics
Speaker: Yanir Rubinstein
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Abstract:

Pursuing a forgotten idea of Calabi, we consider in joint work with B. Clarke the space of Kahler metrics as a Riemannian submanifold of the space of all Riemannian metrics, and study the associated submanifold geometry. In particular, we show that the intrinsic and extrinsic distance functions are equivalent. We also determine the metric completion of the space of Kahler metrics, making contant with recent generalizations of the Calabi-Yau Theorem in pluripotential theory. As an application we obtain a new analytic stability criterion for the existence of a Kahler-Einstein metric in terms of the Ricci flow and the distance function. We also prove that the Kahler-Ricci flow converges as soon as it converges in the (very weak) metric sense.