A first-variation formula for eigenvalue functionals at the essential-spectrum edge characterizes all maximizing weights for Laplace and Steklov problems.
org/abs/2410.13347
2 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.
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Eigenvalue optimization via a first-variation formula
A first-variation formula for eigenvalue functionals at the essential-spectrum edge characterizes all maximizing weights for Laplace and Steklov problems.
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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.