•  
  •  
 

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

The paper contains proof of equicontinuity of the conformal modulus of a condenser in Rn with respect to its α-uniformly perfect plate and the solution of the problem of constructing a lower bound for the conformal capacity of a condenser with α-uniformly perfect plates.

First Page

191

Last Page

212

References

1. Aseev V.V. Continuity of conformal capacity for condensers with uniformly perfect plates. Siberian Mathematical Journal. V. 40, No 2, P. 243-253 (1999).

2. Aseev V.V., Lazareva O.A. On the continuity of the reduced modulus and the transfinite diameter. Russian Mathematics (Izvestiya VUZ. Matematika). No 10(533). Pp. 10-18 (2006).

3. Kuratovsky K. Topology. V. 2. M.: Mir (1969).

4. Lazareva O.A. Capacity properties of uniformly perfect sets and condensers (diss.). Novosibirsk, Novosibirsk State University (2009).

5. Lazareva O.A. Some properties of the reduced modulus in space. Siberian Mathematical Journal. V. 49, No 1, Pp. 145-152 (2008).

6. Reshetnyak Yu.G. Spatial mappings with limited distortion. Novosibirsk: Nauka. (1982).

7. Sychev A.V. Modules and spatial quasi-conformal mappings. Novosibirsk: Nauka, 152 p. (1983).

8. Hausdorff F. Theory of sets. M.: ONTI NKTP USSR (1937).

9. Caraman P. Relations between p-capacity and p-module (II). Rev. Roumaine Math. Pures Appl. V. 39, No 6, Pp. 555-577 (1994).

10. Gehring F.W. Rings and quasiconformal mappings in space. Trans. Amer. Math. Soc. V. 103, No 3, Pp. 353-393 (1962).

11. Gehring F.W. Quasiconformal mappings. Complex Analysis and its Applications. Lect. Int. Semin. Course. Trieste, Vol.2, Vienna, Pp. 213-268 (1976).

12. Gehring F.W. Symmetrization of rings in space. Trans. Amer. Math. Soc. V. 101, No 3, Pp. 499-519 (1961).

13. Hesse J. A p-extremal length and p-capacity equality. Ark. Math. V. 13, No 1, pp. 131-144 (1975).

14. Järvi P., Vuorinen M. Uniformly perfect sets and quasiregular mappings. J. London Math. Soc. Ser. 2. V. 54, No. 174, Part 3, Pp. 515-529 (1996).

15. Michael E. Topology on spaces of subsets. Trans. Amer. Math. Soc. V. 71, No. 1, Pp. 152-182 (1951).

16. Pommerenke Ch. On uniformly perfect sets and Fuchsian groups. Analysis. V. 4, No. 3/4, Pp. 299-321 (1984).

17. Väisälä J. Lectures on n-dimensional quasiconformal mappings. Lect. Notes Math. V. 229, Pp. 1-144 (1971).

18. Väisälä J. Capacity and measure. Michigan Math. J. V. 22, Pp. 1-3 (1975).

19. Väisälä J. On the null-sets for extremal lengths. Ann. Acad. Sci. Fenn. Ser. AI. V. 322, Pp. 1-12 (1962).

20. Vuorinen M. Conformal geometry and quasiregular mappings. Springer-Verlag, Berlin e.a. 209 p. (Lect. Notes Math, V. 1319) (1988).

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.