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Sam Nead
Sam Nead
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As Ian says, this is answered by the Schwarz lemma. The precise statement you want is due to Ahlfors - see here:

is the Wikipedia page for the http://en.wikipedia.org/wiki/Schwarz%E2%80%93Ahlfors%E2%80%93Pick_theoremAhlfors-Schwarz-Pick lemma.

As Ian says, this is answered by the Schwarz lemma. The precise statement you want is due to Ahlfors - see here:

http://en.wikipedia.org/wiki/Schwarz%E2%80%93Ahlfors%E2%80%93Pick_theorem

As Ian says, this is answered by the Schwarz lemma. The precise statement you want is due to Ahlfors - here is the Wikipedia page for the Ahlfors-Schwarz-Pick lemma.

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Sam Nead
Sam Nead
  • 28.2k
  • 5
  • 72
  • 131

As Ian says, this is answered by the Schwarz lemma. The precise statement you want is due to Ahlfors - see here:

http://en.wikipedia.org/wiki/Schwarz%E2%80%93Ahlfors%E2%80%93Pick_theorem