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The Serre duality theorem for a non-compact weighted CR manifold

Authors: Mitsuhiro Itoh, Jun Masamune and Takanari Saotome
Journal: Proc. Amer. Math. Soc. 136 (2008), 3539-3548
MSC (2000): Primary 32V20, 53C17; Secondary 58A14, 14F15
Published electronically: June 11, 2008
MathSciNet review: 2415038
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Abstract: It is proved that the Hodge decomposition and Serre duality hold on a non-compact weighted CR manifold with negligible boundary. A complete CR manifold has negligible boundary. Some examples of complete CR manifolds are presented.

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Additional Information

Mitsuhiro Itoh
Affiliation: Institute of Mathematics, University of Tsukuba, 305-8751, Tsukuba, Japan

Jun Masamune
Affiliation: Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609-2280

Takanari Saotome
Affiliation: Graduate School of Pure and Applied Sciences, University of Tsukuba, 305-8571, Tsukuba, Japan

Keywords: Strongly pseudo-convex manifold, CR manifold, Serre duality, Hodge decomposition, Witten-Kohn Laplacian, weighted Laplacian
Received by editor(s): July 17, 2007
Published electronically: June 11, 2008
Communicated by: Mikhail Shubin
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.