Local Asymmetry and the Inner Radius of Nodal Domains
Spectral Theory
2008-09-05 v4 Analysis of PDEs
Abstract
Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue \lambda. We show that the volume of {f>0} inside any ball B whose center lies on {f=0} is > C|B|/\lambda^n. We apply this result to prove that each nodal domain contains a ball of radius > C/\lambda^n.
Keywords
Cite
@article{arxiv.math/0703663,
title = {Local Asymmetry and the Inner Radius of Nodal Domains},
author = {Dan Mangoubi},
journal= {arXiv preprint arXiv:math/0703663},
year = {2008}
}
Comments
12 pages, 1 figure; minor corrections; to appear in Comm. PDEs