Revista Matemática Iberoamericana

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Volume 24, Issue 1, 2008, pp. 91–116
DOI: 10.4171/RMI/531

Published online: 2008-04-30

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

Stefano Pigola[1], Marco Rigoli[2] and Alberto G. Setti[3]

(1) Università dell'Insubria, Como, Italy
(2) Università di Milano, Italy
(3) Università dell'Insubria, Como, Italy

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.

Keywords: Riemannian vector bundles, harmonic sections, Morse index

Pigola Stefano, Rigoli Marco, Setti Alberto: A finiteness theorem for the space of $L^{p}$ harmonic sections. Rev. Mat. Iberoam. 24 (2008), 91-116. doi: 10.4171/RMI/531