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

 

A note on harmonic forms on complete manifolds


Author: Luen-fai Tam
Journal: Proc. Amer. Math. Soc. 126 (1998), 3097-3108
MSC (1991): Primary 58E20
MathSciNet review: 1459152
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Abstract: In this note, we will prove that under certain conditions, the space of polynomial growth harmonic functions and harmonic forms with a fixed growth rate on manifolds which are asymptotically nonnegatively curved is finite dimensional. This is a partial generalization of the works of Li and Colding-Minicozzi. We will also give an explicit estimate for the dimension in case the manifold is a complete surface of finite total curvature. This is a generalization to harmonic forms of the work of Li and the author.


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Additional Information

Luen-fai Tam
Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
Email: lftam@math.cuhk.edu.hk

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04474-8
PII: S 0002-9939(98)04474-8
Received by editor(s): February 19, 1997
Additional Notes: Research partially supported an Earmarked grant of Hong Kong.
Communicated by: Peter Li
Article copyright: © Copyright 1998 American Mathematical Society