Assouad dimension, Nagata dimension, and uniformly close metric tangents
Assouad dimension, Nagata dimension, and uniformly close metric tangents
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Assouad 尺寸、Nagata 尺寸和一致闭合公制切线
DOI：
10.1512/iumj.2015.64.5469
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
T. Rajala
中科院分区：
文献类型：
--
作者：
E. Donne;T. Rajala
研究了度量空间的Assouad维数和Nagata维数。作为一般结果，我们证明了度量空间的Nagata维度始终由Assouad维度从上到下有界。大部分的文件是致力于研究这些度量维数的度量空间是当地的维数的度量切线。只有一致的切线是不够的。另外还需要的是，切线具有独立于点和切线的均匀常数的维数，或者切线是唯一的。我们将把我们的结果应用于等正则次黎曼流形，并证明局部它们的Nagata维数等于拓扑维数。
We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the dimensions of its metric tangents. Having uniformly close tangents is not sufficient. What is needed in addition is either that the tangents have dimension with uniform constants independent from the point and the tangent, or that the tangents are unique. We will apply our results to equiregular subRiemannian manifolds and show that locally their Nagata dimension equals the topological dimension.