We prove new (sharp) Liouville-type properties via degenerate Hadamard three-sphere theorems for fully nonlinear equations structured over Heisenberg vector fields. As model examples, we cover the case of Pucci’s extremal operators perturbed by suitable semilinear and gradient terms, extending to the Heisenberg setting known contributions valid in the Euclidean framework.

中文翻译：

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Heisenberg群上完全非线性PDE的一些新的Liouville型结果

我们通过退化的Hadamard三球定理证明了构造在Heisenberg向量场上的完全非线性方程组的新（清晰）的Liouville型性质。作为模型示例，我们涵盖了Pucci的极值算子受到适当的半线性和梯度项干扰的情况，并扩展到海森堡，以设定在欧几里得框架内有效的已知贡献。