The Kähler-Ricci flow and stability

Lundi 7 janvier 2008 14:00-15:00 - D.h. phong - Columbia University

Résumé : The Kähler-Ricci flow is the version of Hamilton’s Ricci flow in the case of Kahler metrics. Necessary and sufficient conditions are identified for the convergence of this flow.
These conditions are stability conditions, in the sense that they are related to the K energy and the Hausdorff property of the underlying complex structure. Since the stationary points of the Kähler-Ricci flow are Kähler-Einstein metrics, and since the existence of such metrics has been conjectured by Yau to be equivalent to stability in the sense of geometric invariant theory, this can be interpreted as a partial confirmation of Yau’s conjecture.

Lieu : bât. 425 - 113-115

The Kähler-Ricci flow and stability  Version PDF