Lower bounds on the hausdorff measure of nodal sets

Christopher D. Sogge; Steve Zelditch

doi:10.4310/MRL.2011.v18.n1.a3

Lower bounds on the hausdorff measure of nodal sets

Christopher D. Sogge, Steve Zelditch

Mathematics

Research output: Contribution to journal › Article › peer-review

46 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	25-37
Number of pages	13
Journal	Mathematical Research Letters
Volume	18
Issue number	1
DOIs	https://doi.org/10.4310/MRL.2011.v18.n1.a3
State	Published - Jan 2011

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ASJC Scopus subject areas

General Mathematics

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title = "Lower bounds on the hausdorff measure of nodal sets",

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.",

author = "Sogge, {Christopher D.} and Steve Zelditch",

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N2 - 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.

AB - 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.

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JO - Mathematical Research Letters

JF - Mathematical Research Letters

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Lower bounds on the hausdorff measure of nodal sets

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