Original article

Calculus of Variations and Partial Differential Equations

, Volume 9, Issue 4, pp 277-296

First online:

Bernstein type theorems for higher codimension

  • J. JostAffiliated withMax Planck Institute for Mathematics in the Sciences, D-04103 Leipzig, Germany
  • , Y.L. XinAffiliated withInstitute of Mathematics, Fudan University, Shanghai

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Abstract.

We show a Bernstein theorem for minimal graphs of arbitrary dimension and codimension under a bound on the slope that improves previous results and is independent of the dimension and codimension. The proof depends on the regularity theory for the harmonic Gauss map and the geometry of Grassmann manifolds.