Sharp upper bounds are obtained for the first two nonzero Steklov eigenvalues in dimensions d >= 7 under volume-boundary normalization, derived from optimal weighted Neumann characterizations, plus strict bounds for higher eigenvalues on planar simply connected domains.
Regularity of minimizing harmonic maps into the sphere
3 Pith papers cite this work. Polarity classification is still indexing.
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A criterion for existence of minimizers of Dirac eigenvalues in conformal classes on spin surfaces yields optimal isoperimetric inequalities and a complete characterization of the conformal spectrum on the sphere.
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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Geometric bounds for Steklov and weighted Neumann eigenvalues on Euclidean domains
Sharp upper bounds are obtained for the first two nonzero Steklov eigenvalues in dimensions d >= 7 under volume-boundary normalization, derived from optimal weighted Neumann characterizations, plus strict bounds for higher eigenvalues on planar simply connected domains.
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Conformally critical metrics and optimal bounds for Dirac eigenvalues on spin surfaces
A criterion for existence of minimizers of Dirac eigenvalues in conformal classes on spin surfaces yields optimal isoperimetric inequalities and a complete characterization of the conformal spectrum on the sphere.
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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.