Study of Complex and vector potential theory

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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.