度量空间的渐近秩
The asymptotic rank of metric spaces
摘要：
本文定义并研究了度量空间的渐近秩的概念，并在主要定理中证明了对于一大类空间，渐近秩的特征是高阶填充函数的增长。对于一个真的、余紧的、单连通的测地线度量空间，在Alexandrov意义下的非曲率的渐近秩等于它的欧几里德秩。
英文摘要：
In this article we define and study a notion of asymptotic rank for metric spaces and show in our main theorem that for a large class of spaces, the asymptotic rank is characterized by the growth of the higher filling functions. For a proper, cocompact, simply-connected geodesic metric space of non-curvature in the sense of Alexandrov the asymptotic rank equals its Euclidean rank.
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