MATHEMATICS

The problem of estimating the curvature of the level line under conformal mappings of a circle

I. A. Aleksandrov, S. A. Kopanev

Tomsk State University

Abstract: A task about finding an exact upper estimate for the curvature of level lines on the class $S$ of univalent holomorphic mappings from a unit circle $S$ is justified as a topical one and its well-known partial solutions for subclasses of mappings from $S$ are presented.

Keywords: conformal mapping, level line, curvature, method of internal variations.

UDC: 517.54

Received: 09.10.2013