Schwarz lemma
Let be the open unit disk in the complex plane . Let be a holomorphic function with . Then for all , and . If the equality holds for any or , then is a rotation: with .
This lemma is less celebrated than the bigger guns (such as the Riemann mapping theorem, which it helps prove); however, it is one of the simplest results capturing the “rigidity” of holomorphic functions. No result exists for real functions, of course.
Title | Schwarz lemma |
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Canonical name | SchwarzLemma |
Date of creation | 2013-03-22 12:44:37 |
Last modified on | 2013-03-22 12:44:37 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 8 |
Author | Koro (127) |
Entry type | Theorem |
Classification | msc 30C80 |