Geodesic
On the preservation of generalized reduced modulus under some geometric transformations of domains in the plane
Dalʹnevostočnyj matematičeskij žurnal, Tome 6 (2005) no. 1, pp. 39-56

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

We study necessary and sufficient conditions for the preservation of the generalized reduced modulus under the extension of domain or a part of its boundary. Also, we give such conditions for polarization and dissymmetrization. As applications, the descriptions of extremal configurations in the known inequalities for the inner radii, the Green functions and the Robin functions are obtained. Some of our results supplement the known boundary distortion theorems for univalent regular functions. 
@article{DVMG_2005_6_1_a3,
     author = {V. N. Dubinin and E. G. Prilepkina},
     title = {On the preservation of generalized reduced modulus under some geometric transformations of domains in the plane},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {39--56},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2005_6_1_a3/}
}
TY  - JOUR
AU  - V. N. Dubinin
AU  - E. G. Prilepkina
TI  - On the preservation of generalized reduced modulus under some geometric transformations of domains in the plane
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2005
SP  - 39
EP  - 56
VL  - 6
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2005_6_1_a3/
LA  - ru
ID  - DVMG_2005_6_1_a3
ER  - 
%0 Journal Article
%A V. N. Dubinin
%A E. G. Prilepkina
%T On the preservation of generalized reduced modulus under some geometric transformations of domains in the plane
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2005
%P 39-56
%V 6
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2005_6_1_a3/
%G ru
%F DVMG_2005_6_1_a3
V. N. Dubinin; E. G. Prilepkina. On the preservation of generalized reduced modulus under some geometric transformations of domains in the plane. Dalʹnevostočnyj matematičeskij žurnal, Tome 6 (2005) no. 1, pp. 39-56. http://geodesic.mathdoc.fr/item/DVMG_2005_6_1_a3/