Asymptotics of the Gaussian Curvatures of the Canonical Metric on the Surface

Details Asymptotics of the Gaussian Curvatures of the Canonical Metric on the Surface Asymptotics of the Gaussian Curvatures of the Canonical Metric on the Surface

2006-04-26

arxiv.org/abs/math/0604579v1

Mathematics

Differential Geometry

11 pages. A previous post "The Canonical Metric on a Riemann Surface and Its Induced Metric on Teichm\"{u}ller Space" has been

Scientific paper

We study the canonical metric on a compact Riemann surface of genus at least
two. While it is known that the canonical metric is of nonpositive curvature,
we show that its Gaussian curvatures are not bounded away from zero nor
negative infinity when the surface is close to the compactification divisor of
Riemann's moduli space.

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