Curvature estimates for semi-convex solutions of asymptotic Plateau problem in $\mathbb{H}^{n+1}$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929463407673344 |
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| author | Hong, Han Zhang, Ruijia |
| author_facet | Hong, Han Zhang, Ruijia |
| contents | In this paper, we consider the asymptotic $σ_k$ Plateau problem in hyperbolic space. We establish $C^2$ estimates for semi-convex complete hypersurfaces satisfying constant $σ_k$ curvature with a prescribed asymptotic boundary at the infinity for $2\leq k\leq n-2$ . The result is based on a new crucial concavity inequality derived for hessian equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature estimates for semi-convex solutions of asymptotic Plateau problem in $\mathbb{H}^{n+1}$ Hong, Han Zhang, Ruijia Differential Geometry 53C21, 35J60, 53C40 In this paper, we consider the asymptotic $σ_k$ Plateau problem in hyperbolic space. We establish $C^2$ estimates for semi-convex complete hypersurfaces satisfying constant $σ_k$ curvature with a prescribed asymptotic boundary at the infinity for $2\leq k\leq n-2$ . The result is based on a new crucial concavity inequality derived for hessian equations. |
| title | Curvature estimates for semi-convex solutions of asymptotic Plateau problem in $\mathbb{H}^{n+1}$ |
| topic | Differential Geometry 53C21, 35J60, 53C40 |
| url | https://arxiv.org/abs/2408.09428 |