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

DOI:
https://doi.org/10.1090/S0002-9939-98-04474-8

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:
https://doi.org/10.1090/S0002-9939-98-04474-8

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