A note on harmonic forms on complete manifolds

Tam, Luen-fai

doi:10.1090/S0002-9939-98-04474-8

A note on harmonic forms on complete manifolds
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Proc. Amer. Math. Soc. 126 (1998), 3097-3108 Request permission

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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