刘维尔定理

本文从粒子束的相空间表示法和刘维尔定理出发，介绍了发射度和亮度的物理概念，简单地讨论了束的发射度和相空间密度分布的测量方法。

, . Starting from the phase space representation of particle beam and Liouville 's theorem , this paper presented the physical concepts of emittance and brightness and simply discussed the determination of particle beam emittance and density distribution in the transverse phase space projection .

通过研究完备的、Ricci曲率非负的黎曼流形上的次调和函数的性质，给出了Yau的关于黎曼流形上的刘维尔定理的另一证明。

The property of subharmonic function on any complete Riemannian manifold with nonnegative Ricci curvature was studied , another proof of Yau 's Liouville Theorem on Riemannian manifold can be obtained .

弱化了刘维尔定理的条件，给出了刘维尔定理的一个推广。

This paper weakened the Liouville s theorem conditions , and gives the Liouville theorem of a promotion .