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Intersection Bounds for Nodal Sets of Laplace Eigenfunctions

  • Yaiza Canzani
  • John A. TothEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 269)

Abstract

Let \((M^n,g)\) be a real analytic compact n-dimensional Riemannian manifold and denote by \(\varphi _{\lambda }\) the eigenfunctions of the Laplace operator \(\Delta _g\) with eigenvalue \(\lambda ^2\). We prove that if \(H \subset M\) is a real analytic closed curve for which there exist \(\lambda _0, C>0\) so that \(\Vert \varphi _\lambda \Vert _{L^2(H)} \ge e^{-C \lambda }\) for all \(\lambda >\lambda _0\), then
$$\begin{aligned} \# \{\varphi _\lambda ^{-1}(0) \cap H \} = O (\lambda ). \end{aligned}$$

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA
  2. 2.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

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