亚纯函数值分布与正规族理论已经有130多年历史，前者主要考虑函数取复数值点的分布情况，后者主要考察函数族在球面度量下的紧致性，该理论对于我们进一步研究亚纯函数的性质起着至关重要的作用。因此，我们将从以下几个方面对值分布与正规族理论加以研究：（1）涉及一般小函数的Picard型定理；（2）涉及分担值与分担函数的两族函数的正规定则；（3）关于正规族的球面导数在原点处的精确上界问题；（4）探索值分布与正规族理论在极小曲面Bernstein型定理及其有限定量形式中的应用。

The theory of value distribution and normal families of meromorphic function has a history of 130 years, the former mainly considers the distribution of the points at which functions take some complex numbers, the latter mainly focuses on the compactness of family of functions in the spherical metric, the theory plays a vital role in further study the properties of meromorphic functions. Therefore, we want to study it from the following aspects: (1) the Picard type theorem concerning small functions; (2) normal criterion about two families of meromorphic functions concerning sharing values or functions;(3) the precise upper bound for spherical Derivative at the origin of normal families; (4) explore the application of value distribution and normal family theory in Bernstein type theorem and its corresponding limited quantitative form of minimal surfaces.