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Subjects
32-XX Several complex variables and analytic spaces
32Axx Holomorphic functions of several complex variables
32A19 Normal families of functions, mappings

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A Schwarz lemma for correspondences and applications.

Kaushal Verma (2003)

Publicacions Matemàtiques

A version of the Schwarz lemma for correspondences is studied. Two applications are obtained namely, the 'non-increasing' property of the Kobayashi metric under correspondences and a weak version of the Wong-Rosay theorem for convex, finite type domains admitting a 'non-compact' family of proper correspondences.

An extension of Schwick's theorem for normal families

Yasheng Ye, Xuecheng Pang, Liu Yang (2015)

Annales Polonici Mathematici

In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.

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