Gol'berg A. L.
On the Radius of Injectivity for Generalized Quasiisometries in the Spaces of Dimension Higher Than Two
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.
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.
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.
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.
Ukr. Mat. Zh. - 1991. - 43, № 12. - pp. 1709–1712