Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Catino - Y. Li - Dario D. Monticelli - A. Roncoroni

A Liouville theorem in the Heisenberg group

created by roncoroni on 17 Oct 2023



Inserted: 17 oct 2023
Last Updated: 17 oct 2023

Year: 2023

ArXiv: 2310.10469 PDF


In this paper we classify positive solutions to the critical semilinear elliptic equation in $\mathbb{H}^n$. We prove that they are the Jerison-Lee's bubbles, provided $n=1$ or $n\geq 2$ and a suitable control at infinity holds. The proofs are based on a classical Jerison-Lee's differential identity and on pointwiseintegral estimates recently obtained for critical semilinear and quasilinear elliptic equations in $\mathbb{R}^n$. In particular, the result in $\mathbb{H}^1$ can be seen as the analogue of the celebrated Caffarelli-Gidas-Spruck classification theorem.

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