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arXiv · 2508.13717

The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group

Sebastiano Nicolussi Golo·Francesco Serra Cassano·Mattia Vedovato
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Abstract

In the first Heisenberg group, we study entire, locally Sobolev intrinsic graphs that are stable for the sub-Riemannian area. We show that, under appropriate integrability conditions for the derivatives, the intrinsic graph must be an intrinsic plane, i.e., a coset of a two dimensional subgroup. This result extends \cite{arXiv:1809.04586} beyond the Lipschitz class.

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Sebastiano Nicolussi Golo, Francesco Serra Cassano, Mattia Vedovato. 2025-08-19. The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group. https://arxiv.org/abs/2508.13717

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