Local asymmetry and the inner radius of nodal domains

Dan Mangoubi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


Let M be a closed Riemannian manifold of dimension n. Let φλ be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue λ. We show that the volume of {φλ > 0} ∪ B is ≥ C|B|/λn, where B is any ball centered at a point of the nodal set. We apply this result to prove that each nodal domain contains a ball of radius ≥ C/λn. The results in this paper extend previous results of Nazarov, Polterovich, Sodin and of the author.

Original languageAmerican English
Pages (from-to)1611-1621
Number of pages11
JournalCommunications in Partial Differential Equations
Issue number9
StatePublished - Sep 2008
Externally publishedYes


  • Asymmetry
  • Growth of eigenfunctions
  • Inner radius
  • Nodal domains


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