Dan Mangoubi
Published 2010-10-21, updated 2010-11-01Version 2
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.
Comments: 4 pages; In section 2 an explanation of the basic iteration idea is added; acknowledgments added
Journal: Comm. Partial Differential Equations 36 (2011), no. 12, 2208--2212
Upper bounds of nodal sets for eigenfunctions of eigenvalue problems
The size of the nodal sets for the eigenfunctions of the smooth laplacian
On Kakeya-Nikodym averages, $L^p$-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions
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