Equicontinuity and normality of mappings with integrally bounded p-moduli

الأصل · EN

We consider the generic discrete open mappings in Rⁿ under which the perturbation of extremal lengths of curve collections is controlled integrally via ∫ Q(x)ηᵖ(|x-x₀|) dm(x) with n-1<p<n, where Q is a measurable function on Rⁿ and ∫ᵣ₁ʳ² η(r) dr ≥ 1 for any η on a given interval [r₁,r₂]. We proved that the family of all open discrete mappings of above type is normal under appropriate restrictions on the majorant Q.