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- W1581373162 abstract "At the end of 1960's, Lawrence Zalcman posed a conjecture that the coefficients of univalent functions $f(z) = z + sumlimits_2^infty a_n z^n$ on the unit disk satisfy the sharp inequality $|a_n^2 - a_{2n-1}| le (n-1)^2$, with equality only for the Koebe function. This remarkable conjecture implies the Bieberbach conjecture, investigated by many mathematicians, and still remains a very difficult open problem for all n > 3; it was proved only in certain special cases. We provide a proof of Zalcman's conjecture based on results concerning the plurisubharmonic functionals and metrics on the universal Teichmuller space. As a corollary, this implies a new proof of the Bieberbach conjecture. Our method gives also other new sharp estimates for large coefficients." @default.
- W1581373162 created "2016-06-24" @default.
- W1581373162 creator A5061302215 @default.
- W1581373162 date "2009-07-21" @default.
- W1581373162 modified "2023-09-27" @default.
- W1581373162 title "The Zalcman conjecture and related problems" @default.
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