Convexity of the K-energy on the space of Kähler metrics and uniqueness of extremal metrics
Artikel i vetenskaplig tidskrift, 2017

We establish the convexity of Mabuchi’s K-energy functional along weak geodesics in the space of Kähler potentials on a compact Kähler manifold, thus confirming a conjecture of Chen, and give some applications in Kähler geometry, including a proof of the uniqueness of constant scalar curvature metrics (or more generally extremal metrics) modulo automorphisms. The key ingredient is a new local positivity property of weak solutions to the homogeneous Monge-Ampère equation on a product domain, whose proof uses plurisubharmonic variation of Bergman kernels.

Plurisubharmonic function

Mabuchi funcional

Constant scalar curvature


Robert Berman

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Bo Berndtsson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Journal of the American Mathematical Society

0894-0347 (ISSN) 1088-6834 (eISSN)

Vol. 30 1165-1196