Further Generalizations and Related Results
The Schwarz–Ahlfors–Pick theorem provides an analogous theorem for hyperbolic manifolds.
De Branges' theorem, formerly known as the Bieberbach Conjecture, is an important extension of the lemma, giving restrictions on the higher derivatives of f at 0 in case f is injective; that is, univalent.
The Koebe 1/4 theorem provides a related estimate in the case that f is univalent.
Read more about this topic: Schwarz Lemma
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