A finiteness theorem for the space of $L^p$ harmonic sections

Abstract

In this paper we give a unified and improved treatment to finite dimensionality results for subspaces of $L^p$ harmonic sections of Riemannian or Hermitian vector bundles over complete manifolds. The geometric conditions on the manifold are subsumed by the assumption that the Morse index of a related Schr#x00F6;dinger operator is finite. Applications of the finiteness theorem to concrete geometric situations are also presented.