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Zeitschrift für Analysis und ihre Anwendungen

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Volume 27, Issue 1, 2008, pp. 31–52
DOI: 10.4171/ZAA/1342

Published online: 2008-03-31

On Two-Dimensional Immersions of Prescribed Mean Curvature in Rn

Matthias Bergner[1] and Steffen Fröhlich[2]

(1) Universität Ulm, Germany
(2) TU Berlin, Germany

We consider two-dimensional immersions of disc-type in Rn. 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.

Keywords: Two-dimensional immersions, prescribed mean curvature, higher codimension, curvature estimates

Bergner Matthias, Fröhlich Steffen: On Two-Dimensional Immersions of Prescribed Mean Curvature in Rn. Z. Anal. Anwend. 27 (2008), 31-52. doi: 10.4171/ZAA/1342