Mathematics

On the continuity of extremal length

Kh. V. Navoyan, V. Kh. Navoyan

Yerevan State University

Abstract: In the paper the continuity of one conformal invariant extremal length is considered. A counterexample is constructed disproving the result of P. M. Tamrazov on the continuity of the extremal distance between two sets. Then some sufficient conditions for the continuity are given.

Keywords: extremal length, module of curve family, separated compact subset.

MSC: 31B15; 31C35

Received: 30.12.2012
Accepted: 25.01.2013

Language: English