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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularity of geodesic rays and Monge-Ampère equations


Authors: D. H. Phong and Jacob Sturm
Journal: Proc. Amer. Math. Soc. 138 (2010), 3637-3650
MSC (2010): Primary 31C10, 53B35
Published electronically: May 5, 2010
MathSciNet review: 2661562
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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,\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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Additional Information

D. H. Phong
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: phong@math.columbia.edu

Jacob Sturm
Affiliation: Department of Mathematics, Rutgers University, Newark, New Jersey 07102
Email: sturm@rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10371-2
PII: S 0002-9939(10)10371-2
Received by editor(s): September 23, 2009
Received by editor(s) in revised form: January 8, 2010
Published electronically: May 5, 2010
Additional Notes: This work was partially supported by NSF under grants DMS-07-57372 and DMS-09-05873
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.