论文标题
温ingarten流在里曼尼亚语中
Weingarten Flows in Riemannian Manifolds
论文作者
论文摘要
Given orientable Riemannian manifolds $M^n$ and $\bar M^{n+1},$ we study flows $F_t:M^n\rightarrow\bar M^{n+1},$ called Weingarten flows,in which the hypersurfaces $F_t(M)$ evolve in the direction of their normal vectors with speed given by a function $W$ of their principal curvatures,called weingarten函数是均匀的，单调的，相对于其任何变量增加，并在阳性锥上呈阳性。我们获得了具有等磁初始数据的流量的存在结果，其中HyperSurfaces $ f_t：m^n \ rightArrow \ bar m^{n+1} $都是并行的，而$ \ bar m^{n+1} $是简单地连接的空间形式，或者是不合格类型的级别对称空间。我们证明，回避原则适用于由奇特的Weingarten函数定义的Weingarten流，并且此类流正在嵌入保存。
Given orientable Riemannian manifolds $M^n$ and $\bar M^{n+1},$ we study flows $F_t:M^n\rightarrow\bar M^{n+1},$ called Weingarten flows,in which the hypersurfaces $F_t(M)$ evolve in the direction of their normal vectors with speed given by a function $W$ of their principal curvatures,called a Weingarten function, which is homogeneous, monotonic increasing with respect to any of its variables, and positive on the positive cone. We obtain existence results for flows with isoparametric initial data, in which the hypersurfaces $F_t:M^n\rightarrow\bar M^{n+1}$ are all parallel, and $\bar M^{n+1}$ is either a simply connected space form or a rank-one symmetric space of noncompact type. We prove that the avoidance principle holds for Weingarten flows defined by odd Weingarten functions, and also that such flows are embedding preserving.
