A Remark on Recent Lower Bounds for Nodal Sets
Analysis of PDEs
2011-10-27 v2 Differential Geometry
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1010.4579,
title = {A Remark on Recent Lower Bounds for Nodal Sets},
author = {Dan Mangoubi},
journal= {arXiv preprint arXiv:1010.4579},
year = {2011}
}
Comments
4 pages; In section 2 an explanation of the basic iteration idea is added; acknowledgments added