Study of Complex and vector potential theory

函数理论的领域:我们研究的潜在数量黎曼面R(+)或域D(+)的一个复杂的多方面的移动时(R(+)或D (+)) function-theoretically复杂参数t移动,我们发现他们移动subharmonically t.Field潜在的理论:我们介绍了自然平衡基于电动螺线管磁矢势1 R ^ 3,我们把它应用到研究庞加莱的评论Dirschlt问题的交流方法。非线性偏微分方程领域：在Riemann于1860年关于非线性波动方程的原始论文的基础上，我们将其推广到对角非线性偏微分方程，并用初值条件求解它们。

Field of function theory : We study how the potential quantity of Riemann surface R(+) or domains D(+) of a complex manifold move when they (R(+) or D(+)) move function-theoretically with complex parameter t, and we find that they move subharmonically for t.Field of potential theory : We introduced the nature of equilibrium magnetic vector potential based on the electric solenoid in 1R^3, and we apply it to research Poincare's remark on Dirschlt problem's alternating method.Field of Non-linear partial differential equations : Based on Riemann's original paper in 1860 concerning non-linear wave equation, we generalized it to the diagonalle non-linear partial differential equation and solve them with initialvalue conditions.