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math.AP2022★ 2 cited
On conformal metrics of constant positive curvature in the plane
Walter Bergweiler, Alexandre Eremenko, James Langley
We prove three theorems about solutions of in the plane. The first two describe explicitly all concave and quasiconcave solutions. The third theorem says that the…
math.AP2022★ 3 cited
Rigidity results on Liouville equation
Alexandre Eremenko, Changfeng Gui, Qinfeng Li +1
We give a complete classification of solutions bounded from above of the Liouville equation $$-Δu=e^{2u}\quad\mbox{in}\quad {\mathbf{R}}^2.$$ More generally, solutions in the class…