On the inner radius of a nodal domain

Dan Mangoubi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Let M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue λ. We give upper and lower bounds on the inner radius of the type C/λα(log λ) β. Our proof is based on a local behavior of eigenfunctions discovered by Donnelly and Fefferman and a Poincaré type inequality proved by Maz'ya. Sharp lower bounds are known only in dimension two. We give an account of this case too.

Original languageAmerican English
Pages (from-to)249-260
Number of pages12
JournalCanadian Mathematical Bulletin
Volume51
Issue number2
DOIs
StatePublished - Jun 2008
Externally publishedYes

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