Geodesic
Distortion theorems for univalent functions in multiply-connected domains
Dalʹnevostočnyj matematičeskij žurnal, Tome 9 (2009) no. 1, pp. 140-149

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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},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2009_9_1_a11/}
}
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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/