The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group
Differential Geometry
2025-08-27 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2508.13717,
title = {The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group},
author = {Sebastiano Nicolussi Golo and Francesco Serra Cassano and Mattia Vedovato},
journal= {arXiv preprint arXiv:2508.13717},
year = {2025}
}
Comments
17 pages; Corollary 4.3 and Proof of Theorem A improved