2017
Том 69
№ 9

All Issues

On branch points of three-dimensional mappings with unbounded characteristic of quasiconformality

Sevost'yanov E. A.

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Abstract

For the open discrete mappings f: D \ {b} → R3 of the domain DR3 satisfying relatively general geometric conditions in D \ {b} and having the essential singularity bR3, we prove the following statement. Let y0 belong to R3 \ f (D \ {b}) and let the inner dilatation KI (x, f) and the outer dilatation KΟ (x, f) of the mapping f at a point x satisfy certain conditions. Denote by Bf the set of branch points of f. Then for an arbitrary neighborhood V of the point y0, a set Vf(Bf ) cannot be contained in the set A such that g(A) = I, where I = {tR: |t| < 1} and g : U Rn is a quasiconformal mapping of the domain U Rn such that AU.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 1, pp 84-97.

Citation Example: Sevost'yanov E. A. On branch points of three-dimensional mappings with unbounded characteristic of quasiconformality // Ukr. Mat. Zh. - 2011. - 63, № 1. - pp. 69-79.

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