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arXiv · 1411.1035

Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary

C. D. Sogge·S. Zelditch
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Abstract

We prove that the Cauchy data of Dirichlet or Neumann $\Delta$- eigenfunctions of Riemannian manifolds with concave (diffractive) boundary can only achieve maximal sup norm bounds if there exists a self-focal point on the boundary, i.e. a point at which a positive measure of geodesics leaving the point return to the point. As an application, the Dirichlet or Neumann eigenfunctions of Riemannian manifolds with concave boundary and non-positive curvature never have eigenfunctions whose boundary traces achieve maximal sup norm bounds.

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C. D. Sogge, S. Zelditch. 2014-11-04. Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary. https://arxiv.org/abs/1411.1035

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