Geodesic
Integral representation of the trace on the sphere of a certain class of vector fields, and uniform estimates of stability for quasiconformal mappings of the ball
Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 239-257 
V. I. Semenov. Integral representation of the trace on the sphere of a certain class of vector fields, and uniform estimates of stability for quasiconformal mappings of the ball. Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 239-257. http://geodesic.mathdoc.fr/item/SM_1988_61_1_a17/
@article{SM_1988_61_1_a17,
     author = {V. I. Semenov},
     title = {Integral representation of the trace on the sphere of a~certain class of vector fields, and uniform estimates of stability for quasiconformal mappings of the ball},
     journal = {Sbornik. Mathematics},
     pages = {239--257},
     year = {1988},
     volume = {61},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_1_a17/}
}
TY  - JOUR
AU  - V. I. Semenov
TI  - Integral representation of the trace on the sphere of a certain class of vector fields, and uniform estimates of stability for quasiconformal mappings of the ball
JO  - Sbornik. Mathematics
PY  - 1988
SP  - 239
EP  - 257
VL  - 61
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1988_61_1_a17/
LA  - en
ID  - SM_1988_61_1_a17
ER  - 
%0 Journal Article
%A V. I. Semenov
%T Integral representation of the trace on the sphere of a certain class of vector fields, and uniform estimates of stability for quasiconformal mappings of the ball
%J Sbornik. Mathematics
%D 1988
%P 239-257
%V 61
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1988_61_1_a17/
%G en
%F SM_1988_61_1_a17

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

An integral representation is established for the trace of a vector field on the sphere in terms of a single differential operator. A concrete uniform estimate of stability is obtained for quasiconformal mappings of the ball as a consequence. Bibliography: 8 titles.

[1] Reshetnyak Yu. G., “Otsenki dlya nekotorykh differentsialnykh operatorov s konechnomernym yadrom”, Sib. matem. zhurn., 11:2 (1970), 414–428 | Zbl

[2] Reshetnyak Yu. G., Teoremy ustoichivosti v geometrii i analize, Nauka, Novosibirsk, 1982 | MR

[3] Ahlfors L. V., “Quasiconformal deformations and mappings in $R^n$”, J. Anal. Math., 30 (1976), 74–97 | DOI | MR | Zbl

[4] Belinskii P. P., “O poryadke blizosti prostranstvennogo kvazikonformnogo otobrazheniya k konformnomu”, Sib. matem. zhurn., 14:3 (1973), 475–483 | MR | Zbl

[5] Lavrentev M. A., Belinskii P. P., “Nekotorye problemy geometricheskoi teorii funktsii”, Tr. MIAN, 128, 1972, 34–40 | MR

[6] Semënov V. I., “O ravnomernykh otsenkakh ustoichivosti dlya prostranstvennykh kvazikonformnykh i kvaziizometricheskikh otobrazhenii”, DAN SSSR, 286:2 (1986), 295–297 | MR

[7] Reshetnyak Yu. G., Prostranstvennye otobrazheniya s ogranichennym iskazheniem, Nauka, Novosibirsk, 1982 | MR

[8] Sychev A. V., Moduli i prostranstvennye kvazikonformnye otobrazheniya, Nauka, Novosibirsk, 1983