The article introduces Ahlfors' generalization of Schwarz' lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems concerning the size of images under holomorphic mappings, including celebrated Picard's theorems. The article concludes with a brief insight into the theory of Kobayashi hyperbolic complex manifolds. Although this survey paper does not contain any new results, it may be useful for the beginner in complex analysis to better understands the concept of hyperbolicity in complex geometry.
"The Ahlfors Lemma and Picard's Theorems,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
2, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss2/7