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On the Inner Radius of a Nodal Domain

  • Dan Mangoubi (a1)
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 Cα(log λ)β. 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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References
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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