We consider two-dimensional immersions of disc-type in 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. While in the first chapter we introduce the non-linear elliptic mean curvature systems in a more abstract way, in Chapter 2 these systems

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... e naturally from the differential geometric identities. A variational problem which illustrates the appearance of mean curvature systems as minimal surfaces in certain Riemannian spaces, and an example for our main theorem complete this second part. Chapter 3 presents a detailed proof of our curvature estimate. Essentially we use ideas from [12] (see also [13] and [14]) where the author applies fundamental results on non-linear elliptic systems with quadratic gradient growth which were developed in [6] .