2018
Том 70
№ 8

All Issues

Gol'berg A. L.

Articles: 5
Article (Russian)

On the Radius of Injectivity for Generalized Quasiisometries in the Spaces of Dimension Higher Than Two

Gol'berg A. L., Sevost'yanov E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 2. - pp. 174-184

We consider a class of local homeomorphisms more general than the mappings with bounded distortion. Under these homeomorphisms, the growth of the p-module (n-1 < p ≤ n) of the families of curves is controlled by an integral containing an admissible metric and a measurable function Q. It is shown that, under generic conditions imposed on the majorant Q, this class has a positive radius of injectivity (and, hence, a ball in which every mapping is homeomorphic). Moreover, one of the conditions imposed on Q is not only sufficient but also necessary for existence of a radius of injectivity.

Brief Communications (Russian)

Extremal problems in a class of mappings with bounded integral characteristics

Gol'berg A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 4. - pp. 544-547

We consider mappings with bounded integral characteristics. We construct extremal mappings of plane rings realizing the minimum of these characteristics.

Brief Communications (Ukrainian)

Quasiconformal mappings and radii of normal systems of neighborhoods

Gol'berg A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1566–1568

We establish a new geometric criterion for plane homeomorphisms to belong to the class ofq-quasiconforrnal mappings.

Article (Ukrainian)

Classes of planar topological maps with first generalized derivatives

Gol'berg A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 8. - pp. 1114–1116

We consider the class of planar topological maps with first generalized derivatives. A geometric method for the study of the properties of this class based on the use of regular systems of neighborhoods is given.

Article (Ukrainian)

Mean coefficients of quasiconformality of a pair of domains

Gol'berg A. L., Kud'yavin V. S.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 12. - pp. 1709–1712