论文标题
静电和Riemann表面
Electrostatics and Riemann Surfaces
论文作者
论文摘要
利用几何形式的技术和最简单形式的复杂分析的技术，我们在具有非平凡拓扑的表面上介绍了电场的推导。该分析的副产品是椭圆函数的直观可视化，当它们的论点复杂得分时。这些技术与黎曼表面理论之间的基本联系也得到了解释。我们的目标是为学生和讲师提供一篇有关标准书中未包含的非凡主题的快速参考文章。
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions when their argument is complex-valued. The underlying connections between these techniques and the theory of Riemann surfaces are also explained. Our goal is to provide students and instructors a quick reference article for an extraordinary topic that is not included in the standard books.
