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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.03386 |
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| _version_ | 1866916867612868608 |
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| author | Sroka, Marcin |
| author_facet | Sroka, Marcin |
| contents | We consider Hessian quotient equations in Riemannian setting related to a problem posed by Delanoë and Urbas. We prove unobstructed second order a priori estimate for the real Hessian quotient equation via the maximum principle argument on Riemannian manifolds in dimension two. This is achieved by introducing new test function and exploiting some fine concavity properties of quotient operator. This result demonstrates that there is intriguing difference between the real case and the complex case, as there are known obstructions for $J$-equation in complex geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03386 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on Hessian quotient equations on Riemannian manifolds Sroka, Marcin Differential Geometry Analysis of PDEs 58J05, 35R01 We consider Hessian quotient equations in Riemannian setting related to a problem posed by Delanoë and Urbas. We prove unobstructed second order a priori estimate for the real Hessian quotient equation via the maximum principle argument on Riemannian manifolds in dimension two. This is achieved by introducing new test function and exploiting some fine concavity properties of quotient operator. This result demonstrates that there is intriguing difference between the real case and the complex case, as there are known obstructions for $J$-equation in complex geometry. |
| title | Remarks on Hessian quotient equations on Riemannian manifolds |
| topic | Differential Geometry Analysis of PDEs 58J05, 35R01 |
| url | https://arxiv.org/abs/2501.03386 |