Ukrainian Mathematical Bulletin

Volume 4, Issue 4, 2007 pp. 573-593.

Theory of Moduli, Capacities, and Normal Families of Mappings Admitting Branching

Authors: Evgenii A. Sevost'yanov
Author institution: Institute of Applied Mathematics and Mechanics of NAS of Ukraine, 74 Rosa Luxemburg Str. 83114, Donetsk, Ukraine, sevostyanov@skif.net, e_sevostyanov@rambler.ru, sevostyanov@iamm.ac.donetsk.ua

Summary: In this paper, we study $Q$-mappings that admit branching points, and which are space mappings satisfying moduli inequalities. We prove that a family of open discrete ring $Q$-mappings, which omit a set of positive capacity, is normal under the condition that $Q$ has finite mean oscillation in every point, or has only logarithmic singularities of order not greater than $n-1.$

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