$C^2$ estimates for $k$-Hessian equations and a rigidity theorem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915153513021440 |
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| author | Zhang, Ruijia |
| author_facet | Zhang, Ruijia |
| contents | We derive a concavity inequality for $k$-Hessian operators under the semi-convexity condition. As an application, we establish interior estimates for semi-convex solutions of the $k$-Hessian equations with vanishing Dirichlet boundary and obtain a Liouville-type result. Additionally, we provide new and simple proofs of Guan-Ren-Wang's results on global curvature estimates for $k$-curvature equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^2$ estimates for $k$-Hessian equations and a rigidity theorem Zhang, Ruijia Analysis of PDEs Differential Geometry 35J60, 53C42 We derive a concavity inequality for $k$-Hessian operators under the semi-convexity condition. As an application, we establish interior estimates for semi-convex solutions of the $k$-Hessian equations with vanishing Dirichlet boundary and obtain a Liouville-type result. Additionally, we provide new and simple proofs of Guan-Ren-Wang's results on global curvature estimates for $k$-curvature equations. |
| title | $C^2$ estimates for $k$-Hessian equations and a rigidity theorem |
| topic | Analysis of PDEs Differential Geometry 35J60, 53C42 |
| url | https://arxiv.org/abs/2408.10781 |