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• W1608222009 abstract "It is an open problem in general to prove that there exists a sequence of $$Delta _g$$ -eigenfunctions $$varphi _{j_k}$$ on a Riemannian manifold (M, g) for which the number $$N(varphi _{j_k}) $$ of nodal domains tends to infinity with the eigenvalue. Our main result is that $$N(varphi _{j_k}) rightarrow +infty $$ along a subsequence of eigenvalues of density 1 if (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.
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• W1608222009 creator A5051556693 @default.
• W1608222009 date "2015-06-09" @default.
• W1608222009 modified "2023-10-15" @default.
• W1608222009 title "Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary" @default.
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• W1608222009 doi "https://doi.org/10.1007/s00208-015-1236-6" @default.
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