A new way to Dirichlet problems for minimal surface systems in arbitrary dimensions and codimensions

2015/01/13 by Jing Mao, Mao, Jing
Mathematics · #35K55 #53C21 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1501.02949

openalex publication_date 2015/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, by considering a special case of the spacelike mean curvature flow investigated by Li and Salavessa [6], we get a condition for the existence of smooth solutions of the Dirichlet problem for the minimal surface equation in arbitrary codimension. We also show that our condition is sharper than Wang's in [13, Theorem 1.1] provided the hyperbolic angle θ of the initial spacelike submanifold M₀ satisfies max_M₀\rm coshθ>√(2).

Related

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• The Dirichlet Problem for the Minimal Surface System in Arbitrary Codimension
• An alternative solvability criterion for the Dirichlet problem for the minimal surface equation and an application to the mean curvature flow
• The Dirichlet problem for the α-singular minimal surface equation
• The Dirichlet problem for a prescribed mean curvature equation