The Bernstein problem for Sobolev intrinsic graphs in the Heisenberg group

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.

17 pages; Corollary 4.3 and Proof of Theorem A improved