This is a survey article on Schwarz's lemma and some applications. In particular, we study Schwarz–Pick theorems, Lindelöf's inequality, Poincaré metric on the open unit disk, and a δ,ϵ version of Schwarz's lemma, due to Earle. We also discuss an inequality of Harris. We include a brief discussion on quasiconformal mappings and Schwarz's lemma. We conclude with some applications in Teichmüller theory.
G et al. (Thu,) studied this question.