复杂常微分方程的一致化及其应用
Uniformizing complex ODEs and applications
摘要：
本文给出了亚纯向量场解在其极因子邻域上的定义域的大小估计方法。相应的技术，在某种意义上说，一些众所周知的现象与存在的度量与正曲率的定量版本。这些想法的几个应用提供了包括一种类型的“限制定理”的解决方案的完整的多项式向量场的$\mathbb{C}^n$和障碍的某些（芽）向量场实现的全球全纯向量场上的紧凑的Kähler流形。作为补充，提出了某些经典方程的新方法，并以Halphen方程为例进行了详细说明。
英文摘要：
We introduce a method to estimate the size of the domain of definition of the solutions of a meromorphic vector field on a neighborhood of its pole divisor. The corresponding techniques are, in a certain sense, quantitative versions of some well-known phenomena related to the presence of metrics with positive curvature. Several applications of these ideas are provided including a type of "confinement theorem" for solutions of complete polynomial vector fields on $\mathbb{C}^n$ and obstructions for certain (germs of) vector fields to be realized by a global holomorphic vector field on a compact Kähler manifold. As a complement a new approach to certain classical equations is proposed and detailed in the case of Halphen equations.
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