Viscosity solution to complex Hessian equations on compact Hermitian manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915118786281472 |
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| author | Cheng, Jingrui Xu, Yulun |
| author_facet | Cheng, Jingrui Xu, Yulun |
| contents | We prove the existence of viscosity solutions to complex Hessian equations on a compact Hermitian manifold that satisfy a determinant domination condition. This viscosity solution is shown to be unique when the right hand is strictly monotone increasing in terms of the solution. When the right hand side does not depend on the solution, we reduces it to the strict monotonicity of the solvability constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00953 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Viscosity solution to complex Hessian equations on compact Hermitian manifolds Cheng, Jingrui Xu, Yulun Analysis of PDEs Differential Geometry 32W20, 35J96 We prove the existence of viscosity solutions to complex Hessian equations on a compact Hermitian manifold that satisfy a determinant domination condition. This viscosity solution is shown to be unique when the right hand is strictly monotone increasing in terms of the solution. When the right hand side does not depend on the solution, we reduces it to the strict monotonicity of the solvability constant. |
| title | Viscosity solution to complex Hessian equations on compact Hermitian manifolds |
| topic | Analysis of PDEs Differential Geometry 32W20, 35J96 |
| url | https://arxiv.org/abs/2406.00953 |