Vanishing of cohomology groups and large eigenvalues of the Laplacian on p-forms

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Abstract

For collapsing of closed Riemannian manifolds, the first positive eigenvalue of the Laplacian on p-forms may or may not tend to infinity. In special cases, we show that the existence of the first positive eigenvalue tending to infinity is related to vanishing of cohomology groups of generic fibers.

Original languageEnglish
Pages (from-to)43-57
Number of pages15
JournalMathematische Zeitschrift
Volume250
Issue number1
DOIs
Publication statusPublished - 2005 May 1

ASJC Scopus subject areas

  • Mathematics(all)

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