曲面上的偏微分方程

Partial Differential Equations with Surfaces

旨在讨论三个不同形式的偏微分方程在一个整域扩张上解的存在性、唯一性以及求解使得所有系数皆正项有限和的一种方法.虽然这些方程都是在研究地图在曲面上一种同构分类时发现的,对相关的组合,或代数结构却有些普遍意义.

The purpose of this paper is to discuss the differential equations in three forms： surface no loop, surface no end and surface Euler for the well-definednes on the extension of integrate domain and their solutions in recursions of finite summations with positive terms. Although the foundation of these equations is established from counting the isomorphic classes for a variety of maps on surfaces, universal significance would be seen in a theory with a certain generality of combinatoric or algebraic configurations.