Classification results of Liouville equations and rigidity of Riemannian surfaces

Qianzhong Ou

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arXiv · 2604.27973

Classification results of Liouville equations and rigidity of Riemannian surfaces

Qianzhong Ou

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Abstract

We study the Liouville equation $\triangle u+e^{2u} =0$ in a Riemannian surface $(M, g)$ with nonnegative $Ricci$ curvature. Under some asymptotic lower bound assumptions, we classify all the solutions to this equation, meanwhile we obtain the rigidity results for the ambient manifold. Note that our assumptions are optimal in some sense and differ from the classical assumption of finite total curvature.

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Qianzhong Ou. 2026-04-30. Classification results of Liouville equations and rigidity of Riemannian surfaces. https://arxiv.org/abs/2604.27973

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