亚纯k-微分拟Strebel结构的存在性
On existence of quasi-Strebel structures for meromorphic k-differentials
摘要：
本文从无边界紧致Riemann曲面上Strebel二次微分的经典概念出发，引入了任意阶亚纯微分的拟Strebel结构的概念.证明了在奇点满足一定自然条件的大于2的偶数阶微分都有这样的结构。奇阶微分的情形则完全不同，我们的存在性结果涉及到一些算术条件。我们讨论了与给定微分相关联的拟Stebel结构的集合，并引入了正k-微分的子类。最后，我们提供了一个家庭的例子，正有理微分，并解释其与经典的海涅-Stieltjes理论的线性微分方程多项式系数。
英文摘要：
In this paper, motivated by the classical notion of a Strebel quadratic differential on a compact Riemann surfaces without boundary we introduce the notion of a quasi-Strebel structure for a meromorphic differential of an arbitrary order. It turns out that every differential of even order k exceeding 2 satisfying certain natural conditions at its singular points admits such a structure. The case of differentials of odd order is quite different and our existence result involves some arithmetic conditions. We discuss the set of quasi-Stebel structures associated to a given differential and introduce the subclass of positive k-differentials. Finally, we provide a family of examples of positive rational differentials and explain their connection with the classical Heine-Stieltjes theory of linear differential equations with polynomial coefficients.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
