Geodesic
On a~problem of Polya and Szeg\H o
Lobachevskii journal of mathematics, Tome 9 (2001), pp. 37-46

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We give a new proof of a theorem, which is originally due to Gehring and Pommerenke on the triviality of the extrema set $M_f$ of the inner mapping radius $|f'(\zeta)|(1-|\zeta|^2)$ over the unit disk in the plane, where the Riemann mapping function $f$ satisfies the well-known Nehari univalence criterion. Our main tool is the local bifurcation research of $M_f$ for the level set parametrization $f_r(\zeta)=f(r\zeta)$, $r>0$. 
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     author = {A. V. Kazantsev},
     title = {On a~problem of {Polya} and {Szeg\H} o},
     journal = {Lobachevskii journal of mathematics},
     pages = {37--46},
     publisher = {mathdoc},
     volume = {9},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2001_9_a4/}
}
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A. V. Kazantsev. On a~problem of Polya and Szeg\H o. Lobachevskii journal of mathematics, Tome 9 (2001), pp. 37-46. http://geodesic.mathdoc.fr/item/LJM_2001_9_a4/