A Remark on Recent Lower Bounds for Nodal Sets

Dan Mangoubi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Recently, two papers [2, 9] appeared which give lower bounds on the size of the nodal sets of eigenfunctions. The purpose of this short note is to point out a third method to obtain a power law lower bound on the volume of the nodal sets. Our method is based on the Donnelly-Fefferman growth bound for eigenfunctions and a growth vs. volume relation we proved in [7].

Original languageAmerican English
Pages (from-to)2208-2212
Number of pages5
JournalCommunications in Partial Differential Equations
Issue number12
StatePublished - Dec 2011

Bibliographical note

Funding Information:
I would like to thank Iosif Polterovich for drawing my attention to this problem and for useful discussions. I thank Joseph Bernstein for an illuminating discussion. I am grateful to Leonid Polterovich for valuable remarks on a preliminary version of this note. This work was partially supported by the Israel Science Foundation (grant no. 225/10).


  • Hausdorff measure
  • Lower bound
  • Nodal set


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