A note on harmonic forms on complete manifolds |
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| Authors: | Luen-fai Tam |
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| Affiliation: | Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong |
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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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