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arXiv · 1809.04586

The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group

Sebastiano Nicolussi·Francesco Serra Cassano
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Abstract

We prove that, in the first Heisenberg group $\mathbb{H}$, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of $\mathbb{H}$. Moreover two examples are given for stressing result's sharpness.

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Sebastiano Nicolussi, Francesco Serra Cassano. 2018-09-12. The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group. https://arxiv.org/abs/1809.04586

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