Isolated singularities of conformal hyperbolic metrics

Abstract

J. Nitsche proved that an isolated singularity of a conformal hyperbolic metric is either a conical singularity or a cusp one. We prove by developing map that there exists a complex coordinate $z$ centered at the singularity where the metric has the expression of either $\frac{4{\alpha }^2|z{|}^{2\alpha -2}}{(1-|z{|}^{2\alpha }{)}^2}|\mathrm{d}z{|}^2$ with $\alpha >0$ or $|z{|}^{-2}(\ln |z|{)}^{-2}|dz{|}^2$.

12 pages

Cited by in corpus (4)

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