Abstract
As briefly mentioned at the beginning of the previous chapter, typical geometric applications of Theorem 4.5 are obtained by applying it when the function ψ is the norm of the section of a suitable vector bundle. In appropriate circumstances, the theorem guarantees that certain vector subspaces of such sections are trivial, the main geometric assumption being the existence of a positive solution ϕ of the differential inequality
where a(x) is a lower bound for the relevant curvature term. According to Lemma 3.10 this amounts to requiring that the bottom of the spectrum of the Schrödinger operator −Δ − Ha(x) is non-negative.
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© 2008 Birkhäuser Verlag AG
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(2008). A finite-dimensionality result. In: Vanishing and Finiteness Results in Geometric Analysis. Progress in Mathematics, vol 266. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8642-9_5
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DOI: https://doi.org/10.1007/978-3-7643-8642-9_5
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8641-2
Online ISBN: 978-3-7643-8642-9
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