Abstract
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.
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Acknowledgments
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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Communicated by J. Jost.
The first author is supported financially by the grant \(E\Sigma \Pi A\): PE1-417.
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Savas-Halilaj, A., Smoczyk, K. Bernstein theorems for length and area decreasing minimal maps. Calc. Var. 50, 549–577 (2014). https://doi.org/10.1007/s00526-013-0646-0
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DOI: https://doi.org/10.1007/s00526-013-0646-0