arXiv math/05113292005-11math.SPmath.AP

On the Inner Radius of Nodal Domains

Dan Mangoubi

备注：: Reference added, slight change in estimate in theorem 1, remark on the new proof in dim two added, to appear in Canad. Math. Bull
发表信息：: Canad. Math. Bull. 51 (2008), no. 2, 249--260

英文摘要：

Let M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue λ. We give upper and lower bounds on the inner radius of the type C/λ^k. Our proof is based on a local behavior of eigenfunctions discovered by Donnelly and Fefferman, and a Poincaré type inequality proved by Maz'ya. Sharp lower bounds are known only in dimension two. We give an account of this case too.

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