Geometry & Topology Seminar

Long Li, McMaster University

“On the convexity of the Mabuchi energy functional along geodesics”

It is conjectured by X.X. Chen that the Mabuchi energy functional is convex along the geodesic connecting two Kaehler metrics, during his study in uniqueness of csck metrics. Now we can give an affirmative answer to this question in the joint work with X.X. Chen and Mihai Paun. The first breakthrough in this subject is the work by Berman and Berndtsson last year, where they proved the weak convexity of the Mabuchi energy functional based on the log-subharmonicity of Bergman kernels. Our work is somewhat a ”global version” of Bergman kernels approximation, and also completes the conjecture by proving the continuity of the Mabuchi energy functional along the geodesic. Finally, we also calculated the almost convexity of the Mabuchi energy functional along the εapproximation geodesics.

MC 5413

**Please Note Room Change for Remainder of Term**