Analytic inequalities, and rough isometries between non-compact Riemannian manifolds
Analytic inequalities, and rough isometries between non-compact Riemannian manifolds
复制标题
非紧黎曼流形之间的解析不等式和粗略等距
DOI：
10.1007/bfb0075650
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发表时间：
1986
影响因子：
1.7
通讯作者：
M. Kanai
中科院分区：
文献类型：
--
作者：
M. Kanai
对于一个非紧黎曼流形，它在无穷远处如何展开是我们必须研究的最有趣的问题之一，而且，在这个蓬特下，它的局部几何和拓扑对我们来说是无关紧要的。粗糙等距的概念是在[K1]中引入的：定义。一张地图：度量空间X和Y之间的X-Y称为粗等距，如果满足以下两个条件：（i）对于足够大的E：> 0，ep在Y中的像的e-邻域与Y本身重合;（ii）存在常数a 2：1和B 2：使得对所有X1，X2 ∈ X.
For a non-compact riemannian manifold, how it spreads at infinity is one of the most interesting problems we have to study, and, in this pont of view, its local geometry and topology are of no matter to us. The notion of rough isometry was introduced in [Kl] in this spirit:Definition. A map ep: X-Y, not necessarily continuous, between metric spaces X and Y, is called a rough isometry, if the following two conditions are satisfied:(i) for a sufficiently large E:> 0, the e-neighborhood of the image of ep in Y coincides with Y itself;(ii) there are constants a 2: 1 and b 2: such that for all Xl, X2 E X.