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

 

On the critical points of the $ E_k$ functionals in Kähler geometry


Author: Valentino Tosatti
Journal: Proc. Amer. Math. Soc. 135 (2007), 3985-3988
MSC (2000): Primary 32Q20, 58E11
Published electronically: September 12, 2007
MathSciNet review: 2341949
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Abstract: We prove that a Kähler metric in the anticanonical class, that is a critical point of the functional $ E_k$ and has nonnegative Ricci curvature, is necessarily Kähler-Einstein. This partially answers a question of X.X. Chen.


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Additional Information

Valentino Tosatti
Affiliation: Department of Mathematics, Harvard University, 1 Oxford St, Cambridge, Massachusetts 02138
Email: tosatti@math.harvard.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08962-9
PII: S 0002-9939(07)08962-9
Received by editor(s): May 8, 2006
Received by editor(s) in revised form: October 2, 2006
Published electronically: September 12, 2007
Additional Notes: The author is supported by a Harvard Mathematics Department grant
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.