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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Xiaodong Wang
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

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