Analysis reveals that stable intrinsic graphs must be intrinsic planes in the Heisenberg group, suggesting new integrability conditions.
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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Golo et al. (2025) studied this question.
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