论文标题
对Krzyz的猜想的新外观
A new look at Krzyz's conjecture
论文作者
论文摘要
最近，作者提出了一种解决几何函数理论的极端问题的新方法。它涉及刺破riemann表面的Teichmuller空间的bers同构定理。 我们在这里表明，这种方法与准形式理论相结合，也可以应用于$ h^\ infty $的非散布霍明型功能。特别是，这证明了旧的开放krzyz猜想此类功能及其概括。 单位球$ h_1^\ $ h^\ infty $自然嵌入了通用的teichmuller空间中，并且h_1^\ infty $中的功能$ f \被视为单位磁盘中单价功能的Schwarzian衍生物。
Recently the author has presented a new approach to solving extremal problems of geometric function theory. It involves the Bers isomorphism theorem for Teichmuller spaces of punctured Riemann surfaces. We show here that this approach, combined with quasiconformal theory, can be also applied to nonvanishing holomorphic functions from $H^\infty$. In particular this gives a proof of an old open Krzyz conjecture for such functions and of its generalizations. The unit ball $H_1^\infty$ of $H^\infty$ is naturally embedded into the universal Teichmuller space, and the functions $f \in H_1^\infty$ are regarded as the Schwarzian derivatives of univalent functions in the unit disk.
