Hypersurfaces of constant sum Hessian curvature in Hyperbolic space
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909718028484608 |
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| author | Yang, Jianbo Lu, Yueming |
| author_facet | Yang, Jianbo Lu, Yueming |
| contents | In this paper, we study the asymptotic Plateau problem in hyperbolic space for constant sum Hessian curvature. More precisely, given a asymptotic boundary $Γ$, one seeks a complete hypersurface $Σ$ in $\mathbb{H}^{n+1}$ satisfying $σ_{n-1}(κ)+ασ_{n}(κ)=σ\in (0,n),\,\,\partial Σ=Γ$ where $α$ is a non-negative number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypersurfaces of constant sum Hessian curvature in Hyperbolic space Yang, Jianbo Lu, Yueming Differential Geometry In this paper, we study the asymptotic Plateau problem in hyperbolic space for constant sum Hessian curvature. More precisely, given a asymptotic boundary $Γ$, one seeks a complete hypersurface $Σ$ in $\mathbb{H}^{n+1}$ satisfying $σ_{n-1}(κ)+ασ_{n}(κ)=σ\in (0,n),\,\,\partial Σ=Γ$ where $α$ is a non-negative number. |
| title | Hypersurfaces of constant sum Hessian curvature in Hyperbolic space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.22375 |