The convergence of boundary expansions and the analyticity of minimal surfaces in the hyperbolic space

2018/01/25 by Han, Qing, Jiang, Xumin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.08348

Abstract

We study expansions near the boundary of solutions to the Dirichlet problem for minimal graphs in the hyperbolic space and prove the local convergence of such expansions if the boundary is locally analytic. As a consequence, we prove a conjecture by F.-H. Lin that the minimal graph is analytic up to the boundary if the boundary is analytic and the minimal graph is smooth up to the boundary.

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