On Two-Dimensional Immersions of Prescribed Mean Curvature in ${\mathbb{R}}^n$

Abstract

We consider two-dimensional immersions of disc-type in ${\mathbb{R}}^n$. We focus on well known classical concepts and study the nonlinear elliptic systems of such mappings. Using an Osserman-type condition we give a-priori estimates of the principle curvatures for graphs with prescribed mean curvature fields and derive a theorem of Bernstein type for minimal graphs.