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- W1989156776 abstract "Let $mathbb D = {z : |z| < 1}$ be the unit disk in the complex plane and denote by $dmathcal A$ two-dimensional Lebesgue measure on $mathbb D$. For $epsilon > 0$ we define $sum_epsilon = z:|$ arg $z | < epsilon$. We prove that for every $epsilon > 0$ there exists a $delta > 0$ such that if $f$ is analytic, univalent and area-integrable on $mathbb D$, and $f(0) = 0$, then $$ int {f^–1(sumepsilon)} | f | dmathcal A > delta int_mathbb D | f | dmathcal A $$ . This problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatations for quasiconformal homeomorphisms of $mathbb D$." @default.
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- W1989156776 date "1999-01-01" @default.
- W1989156776 modified "2023-10-01" @default.
- W1989156776 title "The angular distribution of mass by Bergman functions" @default.
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- W1989156776 doi "https://doi.org/10.4171/rmi/251" @default.
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