Concentration of eigenfunctions near a concave boundary

Sinan Ariturk

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arXiv · 1007.0231

Concentration of eigenfunctions near a concave boundary

Sinan Ariturk

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Abstract

This paper concerns the concentration of Dirichlet eigenfunctions of the Laplacian on a compact two-dimensional Riemannian manifold with strictly geodesically concave boundary. We link three inequalities which bound the concentration in different ways. We also prove one of these inequalities, which bounds the L^p norms of the restrictions of eigenfunctions to broken geodesics.

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Sinan Ariturk. 2011-10-31. Concentration of eigenfunctions near a concave boundary. https://arxiv.org/abs/1007.0231

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