# A negative answer to a one-dimensional symmetry problem in the Heisenberg group

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In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group $${\mathbb{H}^n=\mathbb{C}^n \times \mathbb{R}}$$ is provided by the unitary group U( n) Ã— {1} and its appropriate...