Complete manifolds with bounded curvature and spectral gaps

Richard Schoen, Hung Tran

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius. We give general conditions which imply that their essential spectrum has an arbitrarily large finite number of gaps. In particular, for any noncompact covering of a compact manifold, there is a metric on the base so that the lifted metric has an arbitrarily large finite number of gaps in its essential spectrum. Also, for any complete noncompact manifold with bounded curvature and positive injectivity radius we construct a metric uniformly equivalent to the given one (also of bounded curvature and positive injectivity radius) with an arbitrarily large finite number of gaps in its essential spectrum.

Original languageEnglish
Pages (from-to)2584-2606
Number of pages23
JournalJournal of Differential Equations
Volume261
Issue number4
DOIs
StatePublished - Aug 15 2016

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