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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 $ L^2$ cohomology of ACH Kähler manifolds


Author: Xiaodong Wang
Journal: Proc. Amer. Math. Soc. 135 (2007), 2949-2960
MSC (2000): Primary 53C55; Secondary 58J50
Published electronically: February 9, 2007
MathSciNet review: 2317973
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Abstract: We discuss a class of complete Kähler manifolds which are asymptotically complex hyperbolic near infinity. The main result is a sharp vanishing theorem for the second $ L^2$ cohomology of such manifolds under certain assumptions. The borderline case characterizes a Kähler-Einstein manifold constructed by Calabi.


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Additional Information

Xiaodong Wang
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: xwang@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08838-7
PII: S 0002-9939(07)08838-7
Received by editor(s): January 17, 2006
Received by editor(s) in revised form: May 24, 2006
Published electronically: February 9, 2007
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2007 American Mathematical Society