On convergence and compactness of space homeomorphisms

2012/07/05 by Vladimir Ryazanov, Evgeny Sevost’yanov, Ryazanov, Vladimir +1 · 1 citation
Mathematics · #30C62 #30C65 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1207.1231

openalex publication_date 2012/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Various theorems on convergence of general space homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring Q--homeomorphisms are obtained. In particular, it was established by us that a family of all ring Q--homeomorphisms f in \Bbb Rⁿ fixing two points is compact provided that the function Q is of finite mean oscillation. These results will have wide applications to Sobolev's mappings.

Citations

• On mappings in the Orlicz-Sobolev classes
• On functions of bounded mean oscillation

Cited by

• On uniformly lightness of ring mappings and convergence to a homeomorphism

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