Mathematical Sciences: Problems in Complex Analysis

这个项目涉及复杂的几个问题 这些变量本身是有意义的， 与平面集合的几何问题有关。 第一组问题涉及迭代理论， 平面上的亚纯函数 提出的主要问题 这里的研究要求，如果任何有理函数的Julia集和 一个合适的整函数或亚纯函数的一致性 完美了 这就等于问Julia集是否有一个 其对数局部密度的一致下界 容量 第二组问题涉及的是 平面上的收敛群在什么情况下 拓扑共轭到Moebius群。 第三组问题涉及分析的研究。 马尔可夫过程理论中的不等式。

This project is concerned with several problems in complex variables that are of interest in their own right and in connection with problems in the geometry of planar sets. The first set of problems deals with the iteration theory of meromorphic functions in the plane. The main question proposed for study here asks if the Julia set of any rational function and of a suitable entire or meromorphic function is uniformly perfect. This is tantamount to asking if the Julia set has a uniform lower bound for the local density of its logarithmic capacity. The second set of problems deals with the question of under what circumstances a convergence group in the plane is topologically conjugate to a Moebius group. The third set of problems involves the study of analytic inequalities that arise in the theory of Markov processes.