带边流形

带边流形的内接半径估计及其几何应用

An Estimate of the Inscribed Radius for a Manifold With Boundary and Its Geometric Applications

设f是紧致不带边流形M上的覆盖映射，证明了f是拟双曲覆盖映射的充分必要条件是（I－f＊）为单射且有闭值域。

Let f be a covering mapping of a compact manifold M without boundary . It is shown that the necessary and sufficient condition of the quasi-hyperbolic covering mapping of f is that ( I-f ) is injective and has closed range .

带边流形上向量场的奇点指标公式及其应用

An Index Formula of Singularities of Vector Fields on Manifolds with Boundary and Its Application

（t＋1）等价带边流形的浸入和整齐嵌入

Immersions and neat embeddings of ( t + 1 ) - equivalent manifolds with boundary

，其中K与（？）在带边紧致流形上的Einstein关系

I.e. X (?) K (?) f CK . The Einstein Relation on a Compact Manifold with Boundary

在带边紧致流形上的Einstein关系

The Einstein Relation on a Compact Manifold with Boundary

带边Riemann流形上Laplace算子的第一特征值之估计

The estimate of first eigenvalue of Laplace operator on Riemann manifolds with bounday

带边紧流形上热核的Harnack不等式

Heat kernel Riemannian Manifold , Harnack Inequality

一类带边三维流形的结构

The Structure of a Kind of 3-manifolds with Boundaries

设f为不带边的紧致流形M上的自覆盖映射，本义证明了，若f∈intE（M），则f满足弱公理A。

Suppose that f is a self-covering map of a compact manifold M without boundary . The authors prove that if f ∈ intE ( M ), then f satisfies weak-Axiom A.

整体地，在能量守恒的假定下.这类系统相当于某带边黎曼流形上的台球系统。

Globally , under the assumption of energy conservation , the system behaves like a billiard system over a Riemannian manifold With boundary .