arXiv:1007.0231 Abstract | arXiv Analytics

arXiv:1007.0231 [math.AP]Abstract References Reviews Resources

Concentration of eigenfunctions near a concave boundary

Published 2010-07-01, updated 2011-10-31Version 5

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.

Comments: 32 pages. Made more corrections.arXiv admin note: substantial text overlap with arXiv:1007.0230

Categories: math.AP

Subjects: 58J50, 35P20

Keywords: concentration, compact two-dimensional riemannian manifold, inequalities, dirichlet eigenfunctions, strictly geodesically concave boundary

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