Title: Eigenvalue estimates for the Bochner Laplacian and harmonic forms on complete manifolds

Authors: Nelia Charalambous

Issue: Volume 59 (2010), Issue 1, 183-206

Abstract: We study the set of eigenvalues of the Bochner Laplacian on a geodesic ball of an open manifold $M$, and find lower estimates for these eigenvalues when $M$ satisfies a Sobolev inequality. We show that we can use these estimates to demonstrate that the set of harmonic forms of polynomial growth over $M$ is finite dimensional, under sufficient curvature conditions. We also study in greater detail the dimension of the space of bounded harmonic forms on coverings of compact manifolds.