Refined Asymptotics for Minimal Graphs in the Hyperbolic Space

2017/06/08 by Weiming Shen, Yue Wang, Shen, Weiming +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1706.02432

openalex publication_date 2017/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the boundary behaviors of solutions f to the Dirichlet problem for minimal graphs in the hyperbolic space with singular asymptotic boundaries and characterize the boundary behaviors of f at the points strictly located in the tangent cones at the singular points on the boundary. For n=2, we also obtain a refined estimate of f.

Citations

• The Loewner-Nirenberg problem in singular domains
• Minimal Graphs in the Hyperbolic Space with Singular Asymptotic Boundaries

Related

• Minimal Graphs in the Hyperbolic Space with Singular Asymptotic Boundaries
• The convergence of boundary expansions and the analyticity of minimal surfaces in the hyperbolic space
• Boundary regularity of minimal graphs in the hyperbolic space
• Optimal regularity of minimal graphs in the hyperbolic space
• On the asymptotic behavior of minimal surfaces in H²×R