Regularity of geodesic rays and Monge-Ampere equations

D. H. Phong, Jacob Sturm

Published 2009-08-04Version 1

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.