The range of super - brownian motions on hyperbolic space 雙曲空間上超布朗運動的范圍
On ellipse in hyperbolic spaces 關于雙曲空間中的橢圓
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 摘要在雙曲空間中引進相應的橢圓概念、討論橢圓的方程,并對橢圓的對稱性等幾何性質(zhì)做出細致考察。
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 通過構造輔助邊值問題,建立了各種能量不等式,并利用這些先驗估計,以及banach - saks定理得到了h ~ 1弱解存在性;利用退化橢圓型方程弱解與強解的一致性和已知的先驗估計,還得到h ~ 1弱解的唯一性。