Lower bounds on the hausdorff measure of nodal sets

Christopher D. Sogge, Steve Zelditch

Research output: Contribution to journalArticle

34 Scopus citations

Abstract

Let Nφλ be the nodal hypersurface of a Δ-eigenfunction φλ of eigenvalue λ2 on a smooth Riemannian manifold. We prove that Hn-1(N φλ) ≥ Cλ 7/4-3n/4 . The best previous lower bound was e-Cλ.

Original languageEnglish (US)
Pages (from-to)25-37
Number of pages13
JournalMathematical Research Letters
Volume18
Issue number1
DOIs
StatePublished - Jan 2011

ASJC Scopus subject areas

  • Mathematics(all)

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