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| In this talk I will present a Liouville-type Theorem for a nonlinear problem involving a fractional operator in the Heisenberg group. Very recently Frank, Gonzalez, Monticelli and Tan have established an extension result, analogue to the one of Caffarelli-Silvestre, in the context of CR manifold. Thanks to this result, we can study the nonlocal problem in $\mathbb H^n$, by studying a local Neumann problem in $\mathbb H^n\times \mathbb R^+$. The main tool of the proof of our Liouville-type result relies on the CR-inversion and the moving plane method, adapted to a subriemannian context. This is a joint work with J. Tan. |
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