Conformally critical metrics and optimal bounds for Dirac eigenvalues on spin surfaces
Differential Geometry
2026-04-17 v1 Analysis of PDEs
Spectral Theory
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.
Cite
@article{arxiv.2604.14840,
title = {Conformally critical metrics and optimal bounds for Dirac eigenvalues on spin surfaces},
author = {Pavel Martynyuk},
journal= {arXiv preprint arXiv:2604.14840},
year = {2026}
}