The critical hyperbolic catenoid has Robin nullity 2 in mode |k|=1 and closed-form asymptotic radius r(a) = (3/2)log a + d_∞ + o(1) for large a and square-root degeneration near a=1/2.
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The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.
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Spectral properties of the Dirichlet-to-Neumann map for the Helmholtz equation
The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.