hyperbolic space meaning in English

双曲空间

The range of super - brownian motions on hyperbolic space
双曲空间上超布朗运动的范围
On ellipse in hyperbolic spaces
关于双曲空间中的椭圆
The concept of ellipse is extended to hyperbolic space and the equation is discussed . some geometric data of ellipse , such as symmetries , will be considered
摘要在双曲空间中引进相应的椭圆概念、讨论椭圆的方程，并对椭圆的对称性等几何性质做出细致考察。
The degenerate elliptic problems we shall study is very closely related to rigidity problems arising from infinitesimal isometric deformation , as well as other geometry problem , such as minimal surface in hyperbolic space . in particular , the existence of solution with high order regularity is very important to investigate geometry problems . one would like to know under what conditions the solution of such equations are as smooth as the given data
通过构造辅助边值问题，建立了各种能量不等式，并利用这些先验估计，以及banach - saks定理得到了h ~ 1弱解存在性；利用退化椭圆型方程弱解与强解的一致性和已知的先验估计，还得到h ~ 1弱解的唯一性。