Fully non-linear elliptic equations on compact hyperkähler manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909302255517696 |
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| author | Gentili, Giovanni Vezzoni, Luigi |
| author_facet | Gentili, Giovanni Vezzoni, Luigi |
| contents | We consider a general class of elliptic equations on hypercomplex manifolds which includes the quaternionic Monge-Ampère equation, the quaternionic Hessian equation and the Monge-Ampère equation for quaternionic $(n-1)$-plurisubharmonic functions. We prove that under suitable assumptions the solutions to these equations on hyperkähler manifolds satisfy a $C^{2,α}$ a priori estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fully non-linear elliptic equations on compact hyperkähler manifolds Gentili, Giovanni Vezzoni, Luigi Differential Geometry Analysis of PDEs 35B45, 53C26, 35J60, 32W50 We consider a general class of elliptic equations on hypercomplex manifolds which includes the quaternionic Monge-Ampère equation, the quaternionic Hessian equation and the Monge-Ampère equation for quaternionic $(n-1)$-plurisubharmonic functions. We prove that under suitable assumptions the solutions to these equations on hyperkähler manifolds satisfy a $C^{2,α}$ a priori estimate. |
| title | Fully non-linear elliptic equations on compact hyperkähler manifolds |
| topic | Differential Geometry Analysis of PDEs 35B45, 53C26, 35J60, 32W50 |
| url | https://arxiv.org/abs/2409.00420 |