JournalsrmiVol. 24, No. 1pp. 91–116

A finiteness theorem for the space of LpL^{p} harmonic sections

  • Stefano Pigola

    Università dell'Insubria, Como, Italy
  • Marco Rigoli

    Università di Milano, Italy
  • Alberto G. Setti

    Università dell'Insubria, Como, Italy
A finiteness theorem for the space of $L^{p}$ harmonic sections cover
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Abstract

In this paper we give a unified and improved treatment to finite dimensionality results for subspaces of LpL^{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.

Cite this article

Stefano Pigola, Marco Rigoli, Alberto G. Setti, A finiteness theorem for the space of LpL^{p} harmonic sections. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 91–116

DOI 10.4171/RMI/531