CR Yamabe Equation on the Heisenberg Group via the method of moving spheres

Congwen Liu

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arXiv · 2512.22458

CR Yamabe Equation on the Heisenberg Group via the method of moving spheres

Congwen Liu

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Abstract

In this paper, we classify positive solutions to the CR Yamabe equation on the Heisenberg group $\mathbb{H}^n$. We show that all such solutions are Jerison-Lee bubbles, without imposing any finite-energy or a priori symmetry assumptions. This result can be regarded as an analogue for $\mathbb{H}^n$ of the celebrated Caffarelli-Gidas-Spruck classification theorem in $\mathbb{R}^n$. To establish this, we develop a systematic approach to implement the method of moving spheres in the setting of the Heisenberg group.

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Congwen Liu. 2025-12-27. CR Yamabe Equation on the Heisenberg Group via the method of moving spheres. https://arxiv.org/abs/2512.22458

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