Riemannian manifolds with uniformly bounded eigenfunctions

John A. Toth, Steve Zelditch

Research output: Contribution to journalArticle

32 Scopus citations

Abstract

The standard eigenfunctions ϕ λ = e i⟨λ, x⟩ on flat tori ℝ n /L have L -norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that L -normalized eigenfunctions have uniformly bounded L1-norms. Similar bases exist on other flat manifolds. Does this property characterize flat manifolds? We give an affirmative answer for compact Riemannian manifolds with quantum completely integrable Laplacians.

Original languageEnglish (US)
Pages (from-to)97-132
Number of pages36
JournalDuke Mathematical Journal
Volume111
Issue number1
DOIs
StatePublished - Jan 1 2002

ASJC Scopus subject areas

  • Mathematics(all)

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