Space of Kähler metrics (V)-- Kähler quantization

Abstract

We prove the convergence of geodesic distance during the quantization of the space of Kähler potentials. As applications, this provides alternative proofs of certain inequalities about the K-energy functional in the projective case.

25 pages. Corrected typos. Added section 5.

References in corpus (2)

• Bergman metrics and geodesics in the space of Kähler metrics on toric varieties
• Calabi flow and projective embeddings

Cited by in corpus (7)

• Random Kähler Metrics
• Probability measures related to geodesics in the space of Kähler metrics
• Simple matrix models for random Bergman metrics
• Stability and integration over Bergman metrics
• The K-energy on small deformations of constant scalar curvature Kahler manifolds
• Regularity of geodesic rays and Monge-Ampere equations
• Magnetic Geodesics on the Space of Kähler Potentials