Optimal regularity of minimal graphs in the hyperbolic space

2015/11/03 by Qing Han, Weiming Shen, Han, Qing +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1511.01143

Accepted by Calc. Var. Partial Differential Equations

arxiv created 2015/11/03 · arxiv updated 2015/11/05

Abstract

We discuss the global regularity of solutions f to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain Ω⊂\mathbb Rⁿ has a nonnegative mean curvature and prove an optimal regularity f∈ C^(1)/(n+1)(Ω). We can improve the Hölder exponent for f if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.

Related

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