Regularity of geodesic rays and Monge-Ampere equations

Abstract

It is shown that the geodesic rays constructed as limits of Bergman geodesics from a test configuration are always of class $C^{1,\alpha },0<\alpha <1$. An essential step is to establish that the rays can be extended as solutions of a Dirichlet problem for a Monge-Ampere equation on a Kaehler manifold which is compact.

References in corpus (5)

• The Monge-Ampère operator and geodesics in the space of Kähler potentials
• Bergman metrics and geodesics in the space of Kähler metrics on toric varieties
• Test configurations and Geodesic rays
• Space of Kähler metrics (V)-- Kähler quantization
• Test configurations, large deviations and geodesic rays on toric varieties

Cited by in corpus (1)

• On Pointwise Gradient Estimates for the Complex Monge-Ampere Equation