This preprint was accepted September, 1997.
Contact: A. Yu. Solynin
Abstract:
Let $l_k=\{\arg z=\al_k, r_1\leq|z|\leq r_2\}$,
$k=1,\ldots,n$; $\al_k\in\bold R$,
$0<
r_1<
r_2\leq1$,
$E=\bigcup^n_{k=1}\,l_k$, $E^*=\{z:\arg z^n=0, r_1\leq|z|\leq
r_2\}$, and let $\om_E(z)$ denote the harmonic measure of $E$
with respect to the domain $\{z:|z|<1\}\setminus E$. We prove
the inequality
$$
\om_E(0)\leq\om_{E^*}(0),
$$
that solves the generalized problem of A. A. Gonchar on the
harmonic measure of radial slits. The proofs are based on the
method of dissymmetrization of V. N. Dubinin and on the method
of extremal metric in the form of the problem on the extremal
partition into nonoverlapping domains. Bibliography: 20 titles.
[ Full text: ( .ps.gz) ]