We consider the space of Kahler metrics on a compact Kahler manifold. This space is an infinite dimensional manifold, and admits many natural quantities describing its geometry. For example, it is known that the L^1 Finsler metric on this space has asymptotic growth comparable to the so-called J functional. We obtain sharp inequalities between the large scale asymptotic of the J functional with respect to this L^1 metric. Applications regarding the initial value problem for Mabuchi geodesic rays are presented (joint with K. Smith and E. George).
Tue, 20/04/2021 - 18:00 to 19:00