Geodesic
Distortion theorems for univalent functions in multiply-connected domains
Dalʹnevostočnyj matematičeskij žurnal, Tome 9 (2009) no. 1, pp. 140-149 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The $n$-point distortion theorem for meromorphic and univalent functions in multiply-connected domains is proved. As the corollaries we derive the new estimates for Schwarzian derivatives in an annulus. Also, we get the inequality for derivatives of conformal and univalent mappings of non-overlapping domains on the plane with radial slits similar the Lavrentev inequality. The main results are expressed in terms of Newmann function and capacity of generalized condencers are applied to prove theorems. 
@article{DVMG_2009_9_1_a11,
     author = {E. G. Prilepkina},
     title = {Distortion theorems for univalent functions in multiply-connected domains},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {140--149},
     year = {2009},
     volume = {9},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2009_9_1_a11/}
}
TY  - JOUR
AU  - E. G. Prilepkina
TI  - Distortion theorems for univalent functions in multiply-connected domains
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2009
SP  - 140
EP  - 149
VL  - 9
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DVMG_2009_9_1_a11/
LA  - ru
ID  - DVMG_2009_9_1_a11
ER  - 
%0 Journal Article
%A E. G. Prilepkina
%T Distortion theorems for univalent functions in multiply-connected domains
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2009
%P 140-149
%V 9
%N 1
%U http://geodesic.mathdoc.fr/item/DVMG_2009_9_1_a11/
%G ru
%F DVMG_2009_9_1_a11
E. G. Prilepkina. Distortion theorems for univalent functions in multiply-connected domains. Dalʹnevostočnyj matematičeskij žurnal, Tome 9 (2009) no. 1, pp. 140-149. http://geodesic.mathdoc.fr/item/DVMG_2009_9_1_a11/

[1] P. Duren, M. M. Schiffer, “Robin functions and distortion of capacity under conformal mapping”, Complex Variables, 21 (1993), 189–196 | DOI | MR | Zbl

[2] M. D. O'Neill, R. E. Thurman, “Extremal domains for Robin capacity”, Complex Variables, 41 (2000), 91–109 | DOI | MR | Zbl

[3] V. N. Dubinin, M. Vuorinen, Robin functions and distortion theorems for regular mappings, Reports in Math Univ. of Helsinki, Finland / Preprint 454, 2007, 21 pp. | MR

[4] E. G. Emelyanov, “O kvadratichnykh differentsialakh v mnogosvyaznykh oblastyakh, yavlyayuschikhsya polnymi kvadratami. II”, Zap. nauch. semin. POMI, 350, 2007, 40–51 | MR

[5] D. Karp, E. Prilepkina, “Reduced modules with free boundary and its applications”, Annales Academi Scient. Fen., 34, 2009 (to appear) | MR

[6] V. N. Dubinin, E. G. Prilepkina, “Teoremy iskazheniya dlya funktsii, meromorfnykh i odnolistnykh v krugovom koltse”, Sib. mat. zhurn. (to appear)

[7] V. N. Dubinin, L. V. Kovalev, “Privedennyi modul kompleksnoi sfery”, Zap.nauchn. semin. POMI, 254, 1998, 76–94 | MR

[8] V. N. Dubinin, E. G. Prilepkina, “O sokhranenii obobschennogo privedennogo modulya pri geometricheskikh preobrazovaniyakh ploskikh oblastei”, Dalnevostochnyi matematicheskii zhurnal, 6:1–2 (2005), 39–56

[9] Ky Fan, “Distortion of univalent functions”, J. Math. Anal.and Appl., 66:3 (1978), 626–631 | DOI | MR | Zbl

[10] V. N. Dubinin, E. V. Kostyuchenko, “Ekstremalnye zadachi teorii funktsii, svyazannye s $n$–kratnoi simmetriei”, Zap. nauch. semin. POMI, 276, 2001, 83–111 | MR | Zbl

[11] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR