In mathematics, the Schwarz lemma, named after Hermann Amandus Schwarz, is a result in complex analysis about holomorphic functions from the open unit disk to itself. The lemma is less celebrated than stronger theorems, such as the Riemann mapping theorem, which it helps to prove. It is however one of the simplest results capturing the rigidity of holomorphic functions.
Read more about Schwarz Lemma: Statement, Proof, Schwarz–Pick Theorem, Proof of Schwarz–Pick Theorem, Further Generalizations and Related Results