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Schwarz-Pick Lemma

If $f$ is an analytic map of the Disk $\Bbb{D}$ into $\Bbb{D}$ and $f$ preserves the hyperbolic distance between any two points, then $f$ is a disk map and preserves all distance.


Busemann, H. The Geometry of Geodesics. New York: Academic Press, p. 41, 1955.

© 1996-9 Eric W. Weisstein