Regularity of geodesic rays and Monge-Ampère equations

Phong, D. H.; Sturm, Jacob

doi:10.1090/S0002-9939-10-10371-2

Regularity of geodesic rays and Monge-Ampère equations
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by D. H. Phong and Jacob Sturm PDF

Proc. Amer. Math. Soc. 138 (2010), 3637-3650 Request permission

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-Ampère equation on a Kähler manifold which is compact.

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