Uniqueness for the Nonlocal Liouville Equation in $\mathbb{R}$

Maria Ahrend, Enno Lenzmann

We prove uniqueness of solutions for the nonlocal Liouville equation $$ (-Δ)^{1/2} w = K e^w \quad \mbox{in $\mathbb{R}$} $$ with finite total $Q$-curvature $\int_{\mathbb{R}} K e^…