Global Regularity for minimal graphs over convex domains in hyperbolic space

2019/08/18 by Huaiyu Jian, Li You, Jian, Huaiyu +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1908.06397

openalex publication_date 2019/08/18 · openalex created_date 2019/08/22 · openalex updated_date 2026/07/28

Abstract

In this paper we study the global regularity for the solution to the Dirichlet problem of the equation of minimal graphs over a convex domain in hyperbolic spaces. We find that the global regularity depends only on the convexity of the domain but independent of its smoothness. Basing on the invariance of the problem under translation and rotation transforms, we construct the super-solution to the problem, by which we prove the optimal and accurate global regularity for this problem.

Related

• Optimal regularity of minimal graphs in the hyperbolic space
• Boundary regularity of minimal graphs in the hyperbolic space
• Optimal Regularity of Constant Graphs in Hyperbolic Space
• Refined Asymptotics for Minimal Graphs in the Hyperbolic Space
• Minimal Graphs in the Hyperbolic Space with Singular Asymptotic Boundaries