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arXiv · 0908.0556

Regularity of geodesic rays and Monge-Ampere equations

D. H. Phong·Jacob Sturm
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Abstract

It is shown that the geodesic rays constructed as limits of Bergman geodesics from a test configuration are always of class $C^{1,α}, 0<α<1$. 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.

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D. H. Phong, Jacob Sturm. 2009-08-04. Regularity of geodesic rays and Monge-Ampere equations. https://arxiv.org/abs/0908.0556

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