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arXiv · 1010.4579

A Remark on Recent Lower Bounds for Nodal Sets

Dan Mangoubi
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Abstract

Recently, Sogge-Zelditch and Colding-Minicozzi gave new power law 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 a previous work.

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Dan Mangoubi. 2010-11-01. A Remark on Recent Lower Bounds for Nodal Sets. https://doi.org/10.1080/03605302.2011.558556

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