A finiteness theorem for the space of $L\sp p$ harmonic sections.

In this paper we give a unified and improved treatment to finite dimensionality results for subspaces of Lp 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 Schrödinger operator is finite. Applications of the finiteness theorem to concrete geometric situations are also presented.