A spherical Bernstein theorem for minimal submanifolds of higher codimension

  • J. Jost
  • Y. L. Xin
  • Ling YangEmail author


Combining the tools of geometric analysis with properties of Jordan angles and angle space distributions, we derive a spherical and a Euclidean Bernstein theorem for minimal submanifolds of arbitrary dimension and codimension, under the condition that the Gauss image is contained in some geometrically defined closed region of a Grassmannian manifold. The proof depends on the subharmoncity of an auxiliary function, the Codazzi equations and geometric measure theory.

Mathematics Subject Classification

58E20 53A10 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.School of Mathematical SciencesFudan UniversityShanghaiChina

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