Optimal Regularity of Constant Graphs in Hyperbolic Space

2018/01/26 by Jiang, Xumin, Xiao, Ling
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.08968

Abstract

Inspired by [6, 7], we study the boundary regularity of constant curvature hypersurfaces in the hyperbolic space ℍⁿ⁺¹, which have prescribed asymptotic boundary at infinity. Through constructing the boundary expansions of the solutions, we derive the optimal regularity of the solutions. Moreover, we obtain an equivalent condition that guarantees the smoothness of the solutions.

Related

• Optimal regularity of minimal graphs in the hyperbolic space
• Boundary Expansions for Constant Mean Curvature Surfaces in the Hyperbolic Space
• Hypersurfaces of constant scalar curvature in hyperbolic space with prescribed asymptotic boundary at infinity
• Hypersurfaces of constant curvature in Hyperbolic space
• Boundary regularity of minimal graphs in the hyperbolic space