On the Inner Radius of Nodal Domains

Dan Mangoubi

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On the Inner Radius of Nodal Domains

Dan Mangoubi

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Abstract

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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Dan Mangoubi. 2006-12-20. On the Inner Radius of Nodal Domains. https://arxiv.org/abs/math/0511329

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