Boundary Distortion and the Schwarzian Derivative of a Univalent Function in a Circular Annulus

V. N. Dubinin

Matematičeskie zametki, Tome 113 (2023) no. 6, pp. 827-835.

Résumé

New distortion theorems are proved for holomorphic univalent functions bounded in a circular annulus and preserving one of its boundary components. In particular, inequalities including the Schwarzian derivative at a boundary point of the annulus are established. All results follow from the properties of the conformal capacity of condensers and symmetrization.

Détail

Keywords: univalent function, angular derivative, Schwarzian derivative, condenser capacity, symmetrization.

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