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On the boundary of Kähler cones


Author: Xiangwen Zhang
Journal: Proc. Amer. Math. Soc. 140 (2012), 701-705
MSC (2010): Primary 53B35, 51M99
DOI: https://doi.org/10.1090/S0002-9939-2011-10929-8
Published electronically: June 21, 2011
MathSciNet review: 2846339
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Abstract: We study some geometric properties of a compact Kähler manifold $ (M^n, g)$ under a certain condition on the bisectional curvature. As an application, we give a new proof for an earlier result which asserts that any boundary class of the Kähler cone of $ M^n$ can be represented by a $ C^{\infty}$ closed (1,1) form that is parallel and everywhere nonnegative.


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Additional Information

Xiangwen Zhang
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, H3A 2K6, Canada
Email: xzhang@math.mcgill.ca

DOI: https://doi.org/10.1090/S0002-9939-2011-10929-8
Received by editor(s): October 24, 2010
Received by editor(s) in revised form: December 1, 2010
Published electronically: June 21, 2011
Communicated by: Jianguo Cao
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.