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arXiv · 2206.00161

On the asymptotic Plateau problem in hyperbolic space

Siyuan Lu
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Abstract

In this paper, we solve the asymptotic Plateau problem in hyperbolic space for constant $σ_{n-1}$ curvature, i.e. the existence of a complete hypersurface in $\mathbb{H}^{n+1}$ satisfying $σ_{n-1}(κ)=σ\in (0,n)$ with a prescribed asymptotic boundary $Γ$. The key ingredient is the curvature estimates. Previously, this is only known for $σ_0<σ<n$, where $σ_0$ is a positive constant.

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Siyuan Lu. 2023-02-13. On the asymptotic Plateau problem in hyperbolic space. https://arxiv.org/abs/2206.00161

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