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(gòu)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。