# The Geometry of Maximum Principles and a Bernstein Theorem in Codimension 2

@article{Assimos2018TheGO, title={The Geometry of Maximum Principles and a Bernstein Theorem in Codimension 2}, author={Renan Assimos and J{\"u}rgen Jost}, journal={arXiv: Differential Geometry}, year={2018} }

We develop a general method to construct subsets of complete Riemannian manifolds that cannot contain images of non-constant harmonic maps from compact manifolds. We apply our method to the special case where the harmonic map is the Gauss map of a minimal submanifold and the complete manifold is a Grassmannian. With the help of a result by Allard, we can study the graph case and have an approach to prove Bernstein-type theorems. This enables us to extend Moser's Bernstein theorem to codimension…

## 9 Citations

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