Inserted: 19 feb 2020
Last Updated: 20 jun 2020
Journal: Nonlinear Analysis
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.
Keywords: Heisenberg group, Liouville Theorem, Fully nonlinear equations, Nonlinear degenerate elliptic equations, Hadamard Three-Sphere theorem