The behaviour of solutions of the Gaussian curvature equation near an isolated boundary point

DOI10.1017/S0305004108001618zbMath1157.35372arXiv0801.2866MaRDI QIDQ3542110

Oliver Roth, Daniela Kraus

Publication date: 28 November 2008

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.2866

zbMATH Keywords

Riemannian metricsGaussian curvature equationYau-Ahlfors-Schwarz lemma

Mathematics Subject Classification ID

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

Related Items (9)

A new Schwarz-Pick lemma at the boundary and rigidity of holomorphic maps ⋮ Metrics with conical singularities on the sphere and sharp extensions of the theorems of Landau and Schottky ⋮ Bounded projective functions and hyperbolic metrics with isolated singularities ⋮ On the isolated singularities of the solutions of the Gaussian curvature equation for nonnegative curvature ⋮ Twice-punctured hyperbolic sphere with a conical singularity and generalized elliptic integral ⋮ Sharp lower bounds for the hyperbolic metric of the complement of a closed subset of the unit circle and theorems of Schwarz-Pick-, Schottky- and Landau-type for analytic functions ⋮ The Hurwitz metric ⋮ Isolated singularities of affine special Kähler metrics in two dimensions ⋮ Debye layer in Poisson-Boltzmann model with isolated singularities

Cites Work

• Local boundary regularity of the canonical Einstein-Kähler metric on pseudoconvex domains
• Curvature and uniformization
• Über die isolierten Singularitäten der Lösungen von \(\Delta u = e^ u\)
• Bounded analytic functions and metrics of constant curvature on Riemann surfaces
• The Schwarz lemma for nonpositively curved Riemannian surfaces
• Prescribing curvature on open surfaces
• Prescribed curvature and singularities of conformal metrics on Riemann surfaces
• Asymptotic radial symmetry for solutions of \(\Delta u+e^ u=0\) in a punctured disc
• Correction to ``Asymptotic radial symmetry for solutions of \(\Delta u+e^ u=0\) in a punctured disc
• A boundary version of Ahlfors' lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps
• Derivatives of the hyperbolic density near an isolated boundary point
• Vollständige konforme Metriken und isolierte Singularitäten subharmonischer Funktionen
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• On a Class of Conformal Metrics
• A General Schwarz Lemma for Kahler Manifolds
• The density of the hyperbolic metric near an isolated boundary point
• An Extension of Schwarz's Lemma

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