Calculus of Variations and Partial Differential Equations

, Volume 47, Issue 3, pp 711–737

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

Authors

    • Max Planck Institute for Mathematics in the Sciences
  • Y. L. Xin
    • Institute of MathematicsFudan University
  • Ling Yang
    • Max Planck Institute for Mathematics in the Sciences
    • Institute of MathematicsFudan University
Open AccessArticle

DOI: 10.1007/s00526-012-0533-0

Cite this article as:
Jost, J., Xin, Y.L. & Yang, L. Calc. Var. (2013) 47: 711. doi:10.1007/s00526-012-0533-0

Abstract

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.

Mathematics Subject Classification (1991)

58E2053A10
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© The Author(s) 2012