Hypersurfaces of constant sum Hessian curvature in Hyperbolic space

2025/07/30 by Jianbo Yang, Yang, Jianbo, Yueming Lu +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2507.22375

openalex publication_date 2025/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 ℍⁿ⁺¹ satisfying σ_n-1(κ)+ασ_n(κ)=σ∈ (0,n), ∂ Σ=Γ where α is a non-negative number.

Citations

• Asymptotic Plateau problem for 2-convex hypersurface in ℍ⁴
• Pogorelov type C² estimates for sum Hessian equations
• Curvature estimates for semi-convex solutions of asymptotic Plateau problem in ℍⁿ⁺¹
• Hypersurfaces of constant scalar curvature in hyperbolic space with prescribed asymptotic boundary at infinity
• Hessian estimates for the sigma-2 equation in dimension four
• On the asymptotic Plateau problem in hyperbolic space
• Curvature estimates for hypersurfaces of constant curvature in hyperbolic space
• The global curvature estimate for the n-2 Hessian equation
• The curvature estimates for convex solutions of some fully nonlinear Hessian type equations
• Interior curvature estimates and the asymptotic plateau problem in hyperbolic space
• Hypersurfaces of Constant Curvature in Hyperbolic Space II

Related

• On the asymptotic Plateau problem in hyperbolic space
• Curvature estimates for semi-convex solutions of asymptotic Plateau problem in ℍⁿ⁺¹
• Asymptotic Plateau problem for 2-convex hypersurface in ℍ⁴
• Smooth Solutions to Asymptotic Plateau Type Problem in Hyperbolic Space
• Hypersurfaces of constant scalar curvature in hyperbolic space with prescribed asymptotic boundary at infinity