Value distribution theory is concerned with the position and frequency of solutions of the equation f(z) = a. Here f may be entire, i.e. an everywhere convergent power series or meromorphic, i.e. the ratio of two such series, or a function in some other domains, such as an angle or a disk. Yang Lo’s significant contributions to this area will be highlighted. Some of his important contributions to normal families will also be described.
For any multiply connected domain Ω in ?2, let S be the boundary of the convex hull in H 3 of ?2Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on ?S = ?Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.
In this paper, we prove that the Bers projection of the integrable Teichmller space is holomorphic. By using the Douady-Earle extension, we obtain some characterizations of the integrable Teichmller space as well as the p-integrable asymptotic affine homeomorphism.
Let X = C\{0,1} and X = X\{}. We get a necessary and suficient condition on the position of in X such that X has stable Teichmller mappings. Furthermore, we can formulate all these stable Teichmller mappings. The main result in this paper partially answers a question posed by Kra.
In this paper, we combine the KSS nest constructed by Kozlovski, Shen and van Strien, and the analytic method proposed by Avila, Kahn, Lyubich and Shen to prove the combinatorial rigidity of unicritical maps.
PENG WenJuan 1, & TAN Lei 2 1 School of Mathematical Sciences, Peking University, Beijing 100871, China
We show that the Mandelbrot set for the family of renormalization transformations of 2-dimensional diamond-like hierachical Potts models in statistical mechanics is connected. We also give an upper bound for the Hausdorff dimension of Julia set when it is a quasi-circle.
WANG XiaoGuang 1,QIU WeiYuan 1 , YIN YongCheng 1 , QIAO JianYong 2 & GAO JunYang 2 1 School of Mathematical Sciences, Fudan University, Shanghai 200433, China
