Local Asymmetry and the Inner Radius of Nodal Domains

By Dan Mangoubi. 2007

52 citations recorded by the source corpus.

Let M be a closed Riemannian manifold of dimension n. Let ϕλ be an eigenfunction of the Laplace–Beltrami operator corresponding to an eigenvalue λ. We show that the volume of {ϕλ > 0} ∩ B is ≥C|B|/λ n , where B is any ball centered at a point of the nodal set. We apply this result to prove that each nodal domain contains a ball of radius ≥C/λ n . The results in this paper extend previous results of Nazarov, Polterovich, Sodin and of the author.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6c41b8d8dc44e81e709ef8a5b99ffea42c544140