# On a problem of Polya and Szego

## (*Lobachevskii Journal of Mathematics, Volume IX*)

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'(ζ)( 1 - |ζ|*^{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}(ζ) = f(rζ), *r>0*.