Skip to main content
2 of 2
added 3 characters in body
QGravity
  • 989
  • 4
  • 12

Hyperbolic Metric on a Riemann Surface

From uniformization theorem, it is known that every conformal class of metrics on a genus-$g$ Riemann surface with $n$ punctures such that $2g+n\ge 3$ contains a unique hyperbolic metric. The punctures correspond to the fixed points of the parabolic elements of the associated Fuchsian group. The question is that: what is the explicit local expression of this unique hyperbolic metric for such a surface around a puncture, associated with the fixed point $x$ of a parabolic element? A good reference is highly appreciated.

QGravity
  • 989
  • 4
  • 12