Bernstein theorems for length and area decreasing minimal maps

  • Andreas Savas-HalilajEmail author
  • Knut Smoczyk


In this article we prove Liouville and Bernstein theorems in higher codimension for length and area decreasing maps between two Riemannian manifolds. The proofs are based on a strong elliptic maximum principle for sections in vector bundles, which we also present in this article.

Mathematics Subject Classification (2000)

53C40 53A07 35J47 58J05 



The first author would like to express his gratitude to the Max-Planck Institute for Mathematics in the Sciences for everything that he benefited during the stay at the Institute and in particular to Professor J. Jost for the scientific support. Moreover, the first author would like to thank Dr. B. Hua for many stimulating conversations.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut für Differentialgeometrie and Riemann Center for Geometry and PhysicsLeibniz Universität HannoverHannoverGermany

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