2017
Том 69
№ 9

All Issues

On the openness and discreteness of mappings with unbounded characteristic of quasiconformality

Sevost'yanov E. A.

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Abstract

The paper is devoted to the investigation of the topological properties of space mappings. It is shown that sense-preserving mappings $f : D \rightarrow \overline{\mathbb{R}^n}$ in a domain $D \subset \mathbb{R}^n$, n ≥ 2, which are more general than mappings with bounded distortion, are open and discrete if a function Q corresponding to the control of the distortion of families of curves under these mappings has slow growth in the domain f(D), e.g., if Q has finite mean oscillation at an arbitrary point $y0 \in f(D)$.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 8, pp 1298-1305.

Citation Example: Sevost'yanov E. A. On the openness and discreteness of mappings with unbounded characteristic of quasiconformality // Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1128-1134.

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