A Remark on Recent Lower Bounds for Nodal Sets

Dan Mangoubi

doi:10.1080/03605302.2011.558556

A Remark on Recent Lower Bounds for Nodal Sets

Dan Mangoubi^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

10 Scopus citations

Abstract

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 language	English
Pages (from-to)	2208-2212
Number of pages	5
Journal	Communications in Partial Differential Equations
Volume	36
Issue number	12
DOIs	https://doi.org/10.1080/03605302.2011.558556
State	Published - 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).

Keywords

Hausdorff measure
Lower bound
Nodal set

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10.1080/03605302.2011.558556

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N2 - 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].

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KW - Hausdorff measure

KW - Lower bound

KW - Nodal set

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ER -

A Remark on Recent Lower Bounds for Nodal Sets

Abstract

Bibliographical note

Keywords

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