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arXiv · 2604.07251

Compactness of Solutions to Sub-Elliptic Equations with Potential on the Heisenberg Group

Jiechen Qiang·Zhongwei Tang·Yichen Zhang·Ning Zhou
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Abstract

In this paper, we investigate the compactness of nonnegative solutions to a critical sub-elliptic equation with a nonnegative potential on the Heisenberg group. We establish compactness in all dimensions. Moreover, we show that if a sequence of solutions blows up, both the potential and its sub-Laplacian must vanish at the blow-up point. Our analysis overcomes the inherent geometric and analytical challenges posed by the Heisenberg group, including the degeneracy of the sub-Laplacian, its non-commutative structure, and the anisotropic dilation symmetry.

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Jiechen Qiang, Zhongwei Tang, Yichen Zhang, Ning Zhou. 2026-04-08. Compactness of Solutions to Sub-Elliptic Equations with Potential on the Heisenberg Group. https://arxiv.org/abs/2604.07251

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