Talk page
Title:
The metric completion of the space of Kahler potentials and applications, part 1
Speaker:
Abstract:
In connection with canonical Kahler metrics, the study of the L^2 Riemannian geometry of the space of Kahler potentials goes back to Mabuchi and Donaldson. In the first part of this series of talks we introduce the associated path length metric space and characterize the metric completion. Barring some difficulties, the techniques we use allow greater generality and we will end up characterizing the metric completion of the analogous L^p Finsler geometries instead. In the second part I will show how one can use the L^1 Finsler geometry to resolve a long standing question in Kahler geometry relating properness of Energy functionals to existence of KE metrics on general Fano manifolds.
Link:
Workshop: