Under asymptotic lower bound assumptions, all solutions of the Liouville equation on surfaces with nonnegative Ricci curvature are classified and the ambient manifold is shown to be rigid.
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2026 2verdicts
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Positive weak solutions to p-Laplace equations in cylinders are monotone increasing in the axial direction under positive locally Lipschitz right-hand side.
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Classification results of Liouville equations and rigidity of Riemannian surfaces
Under asymptotic lower bound assumptions, all solutions of the Liouville equation on surfaces with nonnegative Ricci curvature are classified and the ambient manifold is shown to be rigid.
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Monotonicity of non-negative solutions of quasilinear elliptic equations in a cylindrical domain
Positive weak solutions to p-Laplace equations in cylinders are monotone increasing in the axial direction under positive locally Lipschitz right-hand side.