Conformally critical metrics and optimal bounds for Dirac eigenvalues on spin surfaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908970104389632 |
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| author | Martynyuk, Pavel |
| author_facet | Martynyuk, Pavel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14840 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conformally critical metrics and optimal bounds for Dirac eigenvalues on spin surfaces Martynyuk, Pavel Differential Geometry Analysis of PDEs Spectral Theory 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. |
| title | Conformally critical metrics and optimal bounds for Dirac eigenvalues on spin surfaces |
| topic | Differential Geometry Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2604.14840 |