Geodesic
On asymptotic curves and values in the theory of mappings with weighted bounded distortion
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 688-697.

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that a mapping with weighted bounded $(p,q)$-distortion can be extended to the set whose family of asymptotic curves has weighted modulus zero. We also state some results about asymptotic values, in particular, the counterpart to Iversen's theorem for mappings with weighted bounded $(n,n)$-distortion.
Keywords: mapping with weighted bounded $(p,q)$-distortion, asymptotic curve, asymptotic value, singularity, capacity, modulus. 
@article{SEMR_2015_12_a86,
     author = {M. V. Tryamkin},
     title = {On asymptotic curves and values in the theory of mappings with weighted bounded distortion},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {688--697},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a86/}
}
TY  - JOUR
AU  - M. V. Tryamkin
TI  - On asymptotic curves and values in the theory of mappings with weighted bounded distortion
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 688
EP  - 697
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a86/
LA  - en
ID  - SEMR_2015_12_a86
ER  - 
%0 Journal Article
%A M. V. Tryamkin
%T On asymptotic curves and values in the theory of mappings with weighted bounded distortion
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 688-697
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a86/
%G en
%F SEMR_2015_12_a86
M. V. Tryamkin. On asymptotic curves and values in the theory of mappings with weighted bounded distortion. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 688-697. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a86/

[1] Yu. G. Reshetnyak, Space mappings with bounded distortion, Translation of Mathematical Monographs, 73, American Mathematical Society, Providence, RI, 1989 | MR | Zbl

[2] O. Martio, S. Rickman, J. Väisälä, “Distortion and Singularities of Quasiregular Mappings”, Ann. Acad. Sci. Fenn. Ser. A.I., 465 (1970), 1–13 | MR

[3] Math. USSR Sb., 21 (1973) | MR

[4] S. Rickman, Quasiregular Mappings, Springer-Verlag, 1993 | MR | Zbl

[5] A. N. Baykin, S. K. Vodop'yanov, “Capacity estimates, Liouville's theorem, and singularity removal for mappings with bounded $(p,q)$-distortion”, Siberian Math. J., 56:2 (2015), 237–261 | DOI

[6] W. Hurewicz, H. Wallman, Dimension theory, Princeton Mathematical Series, 4, Princeton University Press, 1941 | MR | Zbl

[7] V. G. Maz'ja, Sobolev Spaces, Springer-Verlag, 1985 | MR

[8] J. Heinonen, T. Kilpeläinen, O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Clarendon Press, 1993 | MR | Zbl

[9] E. M. Stein, Harmonic Analysis: Real-Variable Method, Orthogonality, and Oscillatory Integrals, Princeton University Press, 1993 | MR

[10] J. Väisälä, Lectures on n-Dimensional Quasiconformal Mappings, Springer-Verlag, 1971 | MR | Zbl

[11] M. V. Tryamkin, “Modulus inequalities for mappings with weighted bounded $(p,q)$-distortion”, Siberian Math. J., 56:6 (2015) (to appear)

[12] E. A. Sevost'yanov, Investigation of space mappings by the geometric method, Naukova dumka, Kiev, 2014 (in Russian)