On spatial mappings with integral restrictions on the characteristic

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 well-known Sokhotsky–Weierstrass
and Liouville theorems are proved.