Conformal complete metrics with prescribed non-negative Gaussian curvature in \({\mathbb{R}}^ 2\)

DOI10.1007/BF01394420zbMath0592.53034OpenAlexW2070826406MaRDI QIDQ1075607

Patricio Aviles

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143325

zbMATH Keywords

nonlinear elliptic PDEasymptotic behaviourcomplete Riemannian metricCohn-Vossen's inequalityprescribed Gaussian curvature

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Global Riemannian geometry, including pinching (53C20)

Related Items (16)

The conformal plate buckling equation ⋮ The critical asymptotics of scalar curvatures of the conformal complete metrics with negative curvature ⋮ Vortex condensation in the Chern-Simons Higgs model: An existence theorem ⋮ Unnamed Item ⋮ Prescribing topological defects for the coupled Einstein and Abelian Higgs equations ⋮ The \(\operatorname{SU}(3)\) Toda system with multiple singular sources ⋮ Existence and compactness of conformal metrics on the plane with unbounded and sign-changing Gaussian curvature ⋮ Prescribing Chern scalar curvatures on noncompact manifolds ⋮ A Liouville theorem for conformal Gaussian curvature type equations in \({\mathbb{R}}^2\) ⋮ Prescribing Scalar Curvatures on the Conformal Classes of Complete Metrics with Negative Curvature ⋮ Prescribing curvature on open surfaces ⋮ Prescribing Curvature with Negative Total Curvature on Open Riemann Surfaces ⋮ Surfaces with prescribed Gauss curvature ⋮ Critical Points, the Gauss Curvature Equation and Blaschke Products ⋮ Qualitative properties of solutions to some nonlinear elliptic equations in \(\mathbb{R}^2\) ⋮ On conformal deformation of nonpositive curvature on noncompact surfaces

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