On the asymptotic Plateau problem in hyperbolic space

2022/06/01 by Siyuan Lu, Lu, Siyuan · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2206.00161

openalex publication_date 2022/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℍⁿ⁺¹ satisfying σ_n-1(κ)=σ∈ (0,n) with a prescribed asymptotic boundary Γ. The key ingredient is the curvature estimates. Previously, this is only known for σ₀<σ

Cited by

• Hypersurfaces of constant sum Hessian curvature in Hyperbolic space
• Asymptotic Plateau problem for 2-convex hypersurface in ℍ⁴

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• Hypersurfaces of constant sum Hessian curvature in Hyperbolic space
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