Ritt's theorem and the Heins map in hyperbolic complex manifolds

全纯映射的迭代函数系统

Iterated function systems of holomorphic maps

本文推广了Heins定理至左迭代函数系统，并研究了全纯映射的超几何距离不等式及右迭代函数系统相关定理。

Puzzle geometry and rigidity: The Fibonacci cycle is hyperbolic

We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and ``complex bounds'', two generalized polynomial-like maps which admits a topological conjugacy, quasiconformal outside the filled-in Julia set are, indeed, quasiconformally conjugated. The proof uses a new abstract removability-type result for quasiconformal maps, following ideas of Heinonen & Koskela and Kallunki & Koskela, optimized to complex dynamics. As the first application to this new method, we prove that, for …

Gromov双曲域的圆域均匀化

Uniformization of Gromov hyperbolic domains by circle domains

本文证明了黎曼球面上的域为Gromov双曲当且仅当共形等价于均匀圆域，解决了Bonk-Heinonen-Koskela猜想并验证了Koebe猜想，且均匀化映射在Möbius变换下唯一。

Metrics with conical singularities on the sphere and sharp extensions of the theorems of Landau and Schottky

An explicit formula for the generalized hyperbolic metric on the thrice--punctured sphere $¶\backslash \{z_1, z_2, z_3\}$ with singularities of order $α_j \le 1$ at $z_j$ is obtained in all possible cases $α_1+α_2+α_3 >2$. The existence and uniqueness of such a metric was proved long time ago by Picard \cite{Pic1905} and Heins \cite{Hei62}, while explicit formulas for the cases $α_1=α_2=1$ were given earlier by Agard \cite{AG} and recently by Anderson, Sugawa, Vamanamurthy and Vuorinen \cite{A}. We also establish precise and explicit lower bounds for the generalized hyperbolic metric. This ext…