A new approach to some nonlinear geometric equations in dimension two

DOI10.1007/S00526-005-0372-3zbMath1105.35036OpenAlexW2110649950WikidataQ115387744 ScholiaQ115387744MaRDI QIDQ2492662

Xiaodong Wang, Feng Bo Hang

Publication date: 14 June 2006

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-005-0372-3

zbMATH Keywords

constant curvature surfacesLiouville type resultsconstant geodesic curvature

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (14)

Conformal metrics with prescribed gaussian and geodesic curvatures ⋮ Prescribing Gaussian and geodesic curvature on disks ⋮ Uniqueness results on surfaces with boundary ⋮ A double mean field equation related to a curvature prescription problem ⋮ The Liouville equation in an annulus ⋮ The geometric Neumann problem for the Liouville equation ⋮ Prescribing Gaussian curvature on surfaces with conical singularities and geodesic boundary ⋮ Classification and refined singularity of positive solutions for nonlinear Maxwell equations arising in mesoscopic electromagnetism ⋮ On the isolated singularities of the solutions of the Gaussian curvature equation for nonnegative curvature ⋮ Properties of positive solutions to an elliptic equation with negative exponent ⋮ Uniqueness theorems for fully nonlinear conformal equations on subdomains of the sphere ⋮ Singular behavior of an electrostatic-elastic membrane system with an external pressure ⋮ Metrics of constant curvature on a Riemann surface with two corners on the boundary ⋮ The Liouville equation in a half-plane

Cites Work

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• Classification of solutions of some nonlinear elliptic equations
• Asymptotic radial symmetry for solutions of \(\Delta u+e^ u=0\) in a punctured disc
• Classification of conformal metrics on \(\mathbb R^2_+\) with constant Gauss curvature and geodesic curvature on the boundary under various integral finiteness assumptions
• Uniqueness theorems through the method of moving spheres
• Conformally invariant systems of nonlinear PDE of Liouville type
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• A uniqueness theorem for harmonic functions on the upper-half plane

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