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 arXiv:1809.04586 beyond the Lipschitz class.
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