Geometric estimates for the Schwarzian derivative

V. N. Dubinin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 72 (2017) no. 3, pp. 479-511

Résumé

This paper is a survey of results involving the Schwarzian derivative and depending on the geometry of the image of a domain under a holomorphic map. The author's results obtained previously by using the theory of condenser capacity and symmetrization constitute the core of the paper. Inequalities for univalent and multivalent functions are considered both at interior and at boundary points of the domain of definition. Auxiliary results and proofs of some of the theorems are presented. Bibliography: 52 titles.

Détail

Keywords: Schwarzian derivative, holomorphic functions, boundary distortion, condenser capacity, symmetrization.

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