Sevost’yanov, Е. А.
(2012)
On spatial mappings with integral restrictions on the characteristic.
Algebra i analiz, 24 (1).
pp. 117.
Abstract
For a given domain D � Rn, some families F of mappings f : D ! Rn,
n � 2 are studied; such families are more general than the mappings with bounded
distortion. It is proved that a family is equicontinuous if
R1
�0
d�
�[�−1(�)]
1
n−1
= 1,
where the integral depends on each mapping f 2 F, � is a special function, and
�0 > 0 is fixed. Under similar restrictions, removability results are obtained for
isolated singularities of f. Also, analogs of the wellknown Sokhotsky–Weierstrass
and Liouville theorems are proved.
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