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The Bernstein Problem in the Heisenberg Group

Nicola Garofalo·Scott D. Pauls
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Abstract

We establish the following theorem of Bernstein type for the first Heisenberg group: Let S be a C^2 connected H-minimal surface which is a graph over some plane P, then S is either a non-characteristic vertical plane, or its generalized seed curve satisfies a type of constant curvature condition.

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Nicola Garofalo, Scott D. Pauls. 2005-05-13. The Bernstein Problem in the Heisenberg Group. https://arxiv.org/abs/math/0209065

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