On equicontinuity of mappings with branching in the closure of a domain

2015/05/24 by Evgeny Sevost’yanov, Sevost'yanov, Evgeny
Mathematics · #30C65 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1505.06490

openalex publication_date 2015/05/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In the present paper, questions about a local behavior of mappings f:D→ \Bbb Rⁿ, n≥ 2, in D are studied. Under some conditions on a measurable function Q(x), Q:D→ [0, ∞], and boundaries of D and D ^′=f(D), it is showed that a family of open discrete map\-ping f:D→ \Bbb Rⁿ, n≥ 2, with characteristic of quasiconformality Q(x), is equicontinuous in D.

Citations

• Singularities of discrete open mappings with controlled p-module

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