Севостьянов, Е. А.
(2011)
О точках ветвления трехмерных отображений с неограниченной характеристикой квазикомфорности.
Український математичний журнал, 63 (1).
pp. 69-79.
ISSN 1027-3190
Abstract
For open discrete mappings f WD n fbg ! R3 of a domain D � R3 satisfying relatively general
geometric conditions in D n fbg and having an essential singularity at a point b 2 R3; we prove the
following statement: Let a point y0 belong to R3 n f .D n fbg/ and let the inner dilatation KI .x; f /
and outer dilatation KO.x; f / of the mapping f at the point x satisfy certain conditions. Let Bf
denote the set of branch points of the mapping f: Then, for an arbitrary neighborhood V of the point
y0; the set V \f .Bf / cannot be contained in a set A such that g.A/ D I; where I D ft 2 RW jt j < 1g
and gWU ! Rn is a quasiconformal mapping of a domain U � Rn such that A � U:
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