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 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Regularity of geodesic rays and Monge-Ampère equations

Author(s): D. H. Phong; Jacob Sturm
Journal: Proc. Amer. Math. Soc. 138 (2010), 3637-3650.
MSC (2010): Primary 31C10, 53B35
Posted: May 5, 2010
MathSciNet review: 2661562
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Abstract | References | Similar articles | Additional information

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: 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
Posted: 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
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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