A Local Volume Estimate for Nodal Domains of Laplace Eigenfunctions
نویسنده
چکیده
Let M either be a closed real analytic Riemannian manifold or a closed C∞-Riemannian surface. We estimate from below the volume of a nodal domain component in an arbitrary ball, provided that this component enters the ball deeply enough. The proof combines a generalized form of Hadamard’s Three Circles Theorem due to Nadirashvili, Rapid Growth of Eigenfunctions in Narrow Domains and the Donnelly-Fefferman Growth Bound. Our estimate is almost sharp and improves the estimate obtained on smooth manifolds by Donnelly-Fefferman, Chanillo-Muckenhoupt and Lu.
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