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arXiv · 2604.14840

Conformally critical metrics and optimal bounds for Dirac eigenvalues on spin surfaces

Pavel Martynyuk
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Abstract

We study the minimization problem for eigenvalues of the Dirac operator within a fixed conformal class on a closed spin Riemannian manifold. We establish a criterion for the existence of a minimizer for this variational problem, focusing specifically on the case of closed surfaces. Furthermore, we apply our results to derive isoperimetric inequalities for the Dirac operator on the two-dimensional sphere, providing a complete characterization of its conformal spectrum.

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Pavel Martynyuk. 2026-04-16. Conformally critical metrics and optimal bounds for Dirac eigenvalues on spin surfaces. https://arxiv.org/abs/2604.14840

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