Curvature estimates for minimal submanifolds of higher codimension and small G-rank

Jost, J.; Xin, Y. L.; Yang, Ling

doi:10.1090/tran/6782

Curvature estimates for minimal submanifolds of higher codimension and small G-rank
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by J. Jost, Y. L. Xin and Ling Yang PDF

Trans. Amer. Math. Soc. 367 (2015), 8301-8323 Request permission

Abstract:

We obtain new curvature estimates and Bernstein type results for a minimal $n-$submanifold in $\mathbb {R}^{n+m}, m\ge 2$, under the condition that the rank of its Gauss map is at most 2. In particular, this applies to minimal surfaces in Euclidean spaces of arbitrary codimension.

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