A finiteness theorem for the space of $L^{p}$ harmonic sections
Pigola , Stefano ; Rigoli , Marco ; Setti , Alberto G.
Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, p. 91-116 / Harvested from Project Euclid
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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.
Publié le : 2008-04-15
Classification:  Riemannian vector bundles,  harmonic sections,  Morse index,  53C21,  35J60 
@article{1216247097,
     author = {Pigola ,  Stefano and Rigoli ,  Marco and Setti ,  Alberto G.},
     title = {A finiteness theorem for the space of $L^{p}$ harmonic
 sections},
     journal = {Rev. Mat. Iberoamericana},
     volume = {24},
     number = {2},
     year = {2008},
     pages = { 91-116},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1216247097}
}

Pigola ,  Stefano; Rigoli ,  Marco; Setti ,  Alberto G. A finiteness theorem for the space of $L^{p}$ harmonic
 sections. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp.  91-116. http://gdmltest.u-ga.fr/item/1216247097/