METRIC CHARACTERISTICS OF SPACE RING DOMAINS WITH RADIAL SLITS THAT ARE NORMAL IN GROETZSCH'S SENSE

摘要

The paper establishes metric and functional characteristics of p-normal (in Groetzsch 's sense) ring domains with radial slits, 1 < p < +∞. In this note, we continue our investigations of p-normal ring domains in the space case, 1 < p < +∞. As in the plane case p = 2 (see [1]), the proofs are essentially based on the equality of the p-module and the p-capacity of a condenser (see [2]) and also on the method of extremal metric in Fuglede's sense (see [3]). Note that Groetzsch (see [4]) was the first to apply the method of extremal metric methodically, in the form of his method of strips. He used it in studying the extremal properties of normal domains in the plane case. One of these properties underlies the definition of the domains studied in this work.