Local Asymmetry and the Inner Radius of Nodal Domains

Details Local Asymmetry and the Inner Radius of Nodal Domains Local Asymmetry and the Inner Radius of Nodal Domains

2007-03-22

arxiv.org/abs/math/0703663v4

Comm. Partial Differential Equations 33 (2008), no. 9, 1611--1621

Mathematics

Spectral Theory

12 pages, 1 figure; minor corrections; to appear in Comm. PDEs

Scientific paper

10.1080/03605300802038577

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.

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