Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58E20

Retrieve articles in all journals with MSC (1991): 58E20

Additional Information

Luen-fai Tam
Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

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