Fully nonlinear prescribed curvature problems on closed manifolds with negative curvature
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918258645401600 |
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| author | Zhang, Jiaogen |
| author_facet | Zhang, Jiaogen |
| contents | In this manuscript, we investigate fully nonlinear prescribed curvature problems for the modified Schouten tensor on closed Riemannian manifolds with negative curvature. We prove that whenever the corresponding concave elliptic operator satisfies a structural Condition $T$, which encompasses all $O(n)$-invariant Gårding-Dirichlet operator, such prescribed curvature problems are always solvable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06577 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fully nonlinear prescribed curvature problems on closed manifolds with negative curvature Zhang, Jiaogen Differential Geometry Analysis of PDEs In this manuscript, we investigate fully nonlinear prescribed curvature problems for the modified Schouten tensor on closed Riemannian manifolds with negative curvature. We prove that whenever the corresponding concave elliptic operator satisfies a structural Condition $T$, which encompasses all $O(n)$-invariant Gårding-Dirichlet operator, such prescribed curvature problems are always solvable. |
| title | Fully nonlinear prescribed curvature problems on closed manifolds with negative curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2510.06577 |