The parabolic split-type Monge-Ampere on split tangent bundle surfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908884797489152 |
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| author | Jordan, Joshua |
| author_facet | Jordan, Joshua |
| contents | We introduce a parabolic analogue of the elliptic split-type Monge-Ampère equation developed by Fang and the author, extending Streets' twisted Monge-Ampère equation. The resulting equation is fully nonlinear and non-concave. We prove long-time existence for equations whose exponents are not too far apart and give conditions for convergence to the twisted Monge-Ampère when the exponents approach each other. Applications include long-time convergence on Kähler backgrounds and reduction to the twisted Monge-Ampère equation under curvature assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07084 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The parabolic split-type Monge-Ampere on split tangent bundle surfaces Jordan, Joshua Differential Geometry Analysis of PDEs 35K55, 53C55 (Primary) 35B65, 53C56 (Secondary) We introduce a parabolic analogue of the elliptic split-type Monge-Ampère equation developed by Fang and the author, extending Streets' twisted Monge-Ampère equation. The resulting equation is fully nonlinear and non-concave. We prove long-time existence for equations whose exponents are not too far apart and give conditions for convergence to the twisted Monge-Ampère when the exponents approach each other. Applications include long-time convergence on Kähler backgrounds and reduction to the twisted Monge-Ampère equation under curvature assumptions. |
| title | The parabolic split-type Monge-Ampere on split tangent bundle surfaces |
| topic | Differential Geometry Analysis of PDEs 35K55, 53C55 (Primary) 35B65, 53C56 (Secondary) |
| url | https://arxiv.org/abs/2507.07084 |