On the strict convexity of the K-energy
Journal article, 2019

Let (X, L) be a polarized projective complex manifold. We show, by a simple toric one-dimensional example, that Mabuchi's K-energy functional on the geodesically complete space of bounded positive (1, 1)-forms in c(1)(L), endowed with the Mabuchi-Donaldson-Semmes metric, is not strictly convex modulo automorphisms. However, under some further assumptions the strict convexity in question does hold in the toric case. This leads to a uniqueness result saying that a finite energy minimizer of the K-energy (which exists on any toric polarized manifold (X, L) which is uniformly K-stable) is uniquely determined modulo automorphisms under the assumption that there exists some minimizer with strictly positive curvature current.

Author

Robert Berman

University of Gothenburg

Mathematics

Pure and Applied Mathematics Quarterly

1558-8599 (ISSN) 1558-8602 (eISSN)

Vol. 15 4 983-999

Subject Categories

Geometry

Discrete Mathematics

Mathematical Analysis

More information

Latest update

7/29/2020