A regularity theorem establishes that sufficiently regular stationary measures for a variational eigenvalue problem on manifolds are absolutely continuous with densities induced by harmonic maps.
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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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A regularity theorem for stationary measures
A regularity theorem establishes that sufficiently regular stationary measures for a variational eigenvalue problem on manifolds are absolutely continuous with densities induced by harmonic maps.
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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.