Geodesic
Some extremal problems for circular polygons
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 21, Tome 206 (1993), pp. 127-136 
A. Yu. Solynin. Some extremal problems for circular polygons. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 21, Tome 206 (1993), pp. 127-136. http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a10/
@article{ZNSL_1993_206_a10,
     author = {A. Yu. Solynin},
     title = {Some extremal problems for circular polygons},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {127--136},
     year = {1993},
     volume = {206},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The main result of this paper is the solution of the following problem posed by J. Hersch (see [1]): find the maximum of conformal radii in the family of all hyperbolic polygons with $n$, $n\ge3$, sides. It is proved that the maximum is attained on the regular hyperbolic polygon. Bibliography: 5 titles.