Dimension estimate of harmonic forms on complete manifolds

Jui-Tang Ray Chen and Chiung-Jue Anna Sung

Vol. 232 (2007), No. 1, 91–109

DOI: 10.2140/pjm.2007.232.91

Abstract

We consider the space of polynomial-growth harmonic forms. We prove that the dimension of such spaces must be finite and can be estimated if the metric is uniformly equivalent to one with asymptotically nonnegative curvature operator. This implies that the space of harmonic forms of polynomial growth order on the connected sum manifolds with nonnegative curvature operator must be finite-dimensional, which generalizes work of Tam.

Keywords

harmonic forms, curvature operator

Mathematical Subject Classification 2000

Primary: 58A05

Secondary: 58A10

Milestones

Received: 17 April 2006

Accepted: 11 September 2006

Published: 1 September 2007