Yamabe problems for formally self-adjoint, conformally covariant, polydifferential operators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915864386732032 |
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| author | Case, Jeffrey S. |
| author_facet | Case, Jeffrey S. |
| contents | Formally self-adjoint, conformally covariant, polydifferential operators provide a general framework for studying variational problems, such as prescribing the scalar, $Q$-, or $σ_2$-curvatures, within a conformal class. We describe recent progress on Yamabe problems for such operators, including uniqueness results on the sphere and nonuniqueness results in general. We also highlight a number of open questions related to these operators, some of which constitute a possible blueprint for the general solution of the Yamabe problem for polydifferential operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14340 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Yamabe problems for formally self-adjoint, conformally covariant, polydifferential operators Case, Jeffrey S. Differential Geometry Analysis of PDEs Formally self-adjoint, conformally covariant, polydifferential operators provide a general framework for studying variational problems, such as prescribing the scalar, $Q$-, or $σ_2$-curvatures, within a conformal class. We describe recent progress on Yamabe problems for such operators, including uniqueness results on the sphere and nonuniqueness results in general. We also highlight a number of open questions related to these operators, some of which constitute a possible blueprint for the general solution of the Yamabe problem for polydifferential operators. |
| title | Yamabe problems for formally self-adjoint, conformally covariant, polydifferential operators |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2603.14340 |