The Gauss image of entire graphs of higher codimension and Bernstein type theorems

Details The Gauss image of entire graphs of higher codimension and Bernstein type theorems The Gauss image of entire graphs of higher codimension and Bernstein type theorems

2010-09-20

arxiv.org/abs/1009.3901v1

Mathematics

Differential Geometry

28 pages

Scientific paper

Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori estimates for the harmonic Gauss map. The required conditions here are more general than in previous work and they therefore enable us to improve substantially previous results for the Lawson-Osseman problem concerning the regularity of minimal submanifolds in higher codimension and to derive Bernstein type results.

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