The Schwarz-Pick Lemma as a Consequence of the Ahlfors-Schwarz-Pick Lemma
Rafael Benjumea Cejas, Juan Carlos Garc\'ia V\'azquez
TL;DR
This paper provides an elementary proof demonstrating that the Schwarz-Pick Lemma can be derived directly from the Ahlfors-Schwarz-Pick Lemma, clarifying their relationship.
Contribution
It offers a simplified proof showing the Schwarz-Pick Lemma is a consequence of the Ahlfors-Schwarz-Pick Lemma, enhancing understanding of their connection.
Findings
Elementary proof established
Schwarz-Pick Lemma derived from Ahlfors-Schwarz-Pick Lemma
Clarifies the logical relationship between the two lemmas
Abstract
The aim of this article is to give an elementary proof of the fact that the Schwarz-Pick Lemma follows from the Ahlfors-Schwarz-Pick Lemma.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Geometry and complex manifolds