arXiv math/07036632007-03math.SPmath.AP

Local Asymmetry and the Inner Radius of Nodal Domains

Dan Mangoubi

备注：: 12 pages, 1 figure; minor corrections; to appear in Comm. PDEs
发表信息：: Comm. Partial Differential Equations 33 (2008), no. 9, 1611--1621
DOI：: 10.1080/03605300802038577

英文摘要：

Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue λ. We show that the volume of {f>0} inside any ball B whose center lies on {f=0} is > C|B|/λ^n. We apply this result to prove that each nodal domain contains a ball of radius > C/λ^n.

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