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.
org/abs/2402.13121
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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.