English

Equicontinuity and normality of mappings with integrally bounded $p$-moduli

Complex Variables 2013-09-10 v1

Abstract

We consider the generic discrete open mappings in Rn{\mathbb R}^n under which the perturbation of extremal lengths of curve collections is controlled integrally via Q(x)ηp(xx0)dm(x)\int Q(x)\eta^p(|x-x_0|) dm(x) with n1<p<nn-1<p<n, where QQ is a measurable function on Rn{\mathbb R}^n and r1r2η(r)dr1\int\limits_{r_1}^{r_2} \eta(r) dr \ge 1 for any η\eta on a given interval [r1,r2].[r_1,r_2]. We proved that the family of all open discrete mappings of above type is normal under appropriate restrictions on the majorant Q.Q.

Keywords

Cite

@article{arxiv.1309.1826,
  title  = {Equicontinuity and normality of mappings with integrally bounded $p$-moduli},
  author = {Anatoly Golberg and Ruslan Salimov and Evgeny Sevost'yanov},
  journal= {arXiv preprint arXiv:1309.1826},
  year   = {2013}
}