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

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

Abstract

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.
Published
25.02.2015
How to Cite
Gol’berg, A. L., and E. A. Sevost’yanov. “On the Radius of Injectivity for Generalized Quasiisometries in the Spaces of Dimension Higher Than Two”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 2, Feb. 2015, pp. 174-8, http://umj.imath.kiev.ua/index.php/umj/article/view/1972.
Section
Research articles