Variants of Ahlfors' lemma and properties of the logarithmic potentials

2013/04/07 by Tanran Zhang, Zhang, Tanran · 1 citation
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.CV

paper · pdf · doi:10.48550/arxiv.1304.2003

12pages

arxiv created 2013/04/07 · arxiv updated 2013/04/09

Abstract

As a special class of conformal metrics with negative curvatures, SK-metrics play a crucial role in metric spaces. This paper concerns the variants of Ahlfors' lemma in an SK-metric space and gives a higher order derivative formula for the logarithmic potential function, which can be applied for the estimates near the singularity of a conformal metric with negative curvatures.

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• A note on the asymptotic behavior of conformal metrics with negative curvatures near isolated singularities

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