On removal of isolates singularities of open discrete mappings

Ye.A. Sevostianov

doi:10.15421/240718

On removal of isolates singularities of open discrete mappings

Ye.A. Sevostianov (Institute of Applied Mathematics and Mechanics of NAS of Ukraine), https://orcid.org/0000-0001-7892-6186

Abstract

We study mappings with finite distortion in $$$\mathbb{R}^n$$$, $$$n \geqslant 2$$$. For the classes of mappings with branching that satisfy modal inequalities we obtain the set of theorems on removal of isolated singularities.

Full Text:

PDF (Русский)

References

John F., Nirenberg L. "On functions of bounded mean oscillation", Comm. Pure Appl. Маth., 1961; 14: pp. 415-426. doi:10.1002/cpa.3160140317

Ignatiev A., Ryazanov V. "Finite mean distortion in mappings theory", Ukr. matem. visnyk, 2005; 2(3): pp. 395-417. (in Russian)

Kuratowski K. Topology. Vol. 2, 1969. (in Russian)

Martio O., Rickman S., Vaisala J. "Definitions for quasiregular mappings", Ann. Acad. Sci. Fenn. Ser. A1. Math., 1969; 448: pp. 1-40.

Martio O., Rickman S., Vaisala J. "Distortion and singularities of quasiregular mappings", Ann. Acad. Sci. Fenn. Ser. A1., 1970; 465: pp. 1-13.

Martio O., Ryazanov V., Srebro U., Yakubov E. "Mappings with finite length distortion", J. d'Anal. Math., 2004; 93: pp. 215-236. doi:10.1007/BF02789308

Martio O., Ryazanov V., Srebro U., Yakubov E. "On Q-homeomorphisms", Ann. Acad. Sci. Fenn., 2005; 30(1): pp. 49-69.

Reshetniak Yu.G. "Space mappings with bounded distortion", Siberian Math. J., 1967; 8(3): pp. 629-658. (in Russian) doi:10.1007/BF02196429

Reshetniak Yu.G. Space mappings with bounded distortion, Novosibirsk, 1982. (in Russian)

Rickman S. Quasireguiar Mappings, Berlin, 1993.

Ryazanov V., Srebro U., Yakubov E. "Finite mean oscillation and the Beltrami equation", Israel J. Math., 2006; 153: pp. 247-266. doi:10.1007/BF02771785

Saks S. Theory of the Integral, Dover Publ. Inc. New York, 1964.

Vaisala J. Lectures on n-Dimensional Quasiconformal Mappings, LNM 229, Springer-Verlag, 1971.

Whyburn J.T. Analytic topology, AMS, Rhode Island, 1942.