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• W2952859897 abstract "It is an open problem in general to prove that there exists a sequence of $Delta_g$-eigenfunctions $phi_{j_k}$ on a Riemannian manifold $(M, g)$ for which the number $N(phi_{j_k}) $ of nodal domains tends to infinity with the eigenvalue. Our main result is that $N(phi_{j_k}) to infty$ along a subsequence of eigenvalues of density $1$ if the $(M, g)$ is a non-positively curved surface with concave boundary, i.e. a generalized Sinai or Lorentz billiard. Unlike the recent closely related work of Ghosh-Reznikov-Sarnak and of the authors on the nodal domain counting problem, the surfaces need not have any symmetries." @default.
• W2952859897 created "2019-06-27" @default.
• W2952859897 creator A5016842069 @default.
• W2952859897 creator A5051556693 @default.
• W2952859897 date "2014-01-18" @default.
• W2952859897 modified "2023-09-27" @default.
• W2952859897 title "Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary" @default.
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• W2952859897 hasPublicationYear "2014" @default.
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