Assouad Dimension, Nagata Dimension, and Uniformly Close Metric Tangents
Abstract
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 sub-Riemannian manifolds and show that, locally,
their Nagata dimension equals the topological dimension.
Main Authors
Format
Articles
Research article
Published
2015
Series
Subjects
Publication in research information system
Publisher
Indiana University
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201508172681Use this for linking
Review status
Peer reviewed
ISSN
0022-2518
DOI
https://doi.org/10.1512/iumj.2015.64.5469
Language
English
Published in
Indiana University Mathematics Journal
Citation
- Le Donne, E., & Rajala, T. (2015). Assouad Dimension, Nagata Dimension, and Uniformly Close Metric Tangents. Indiana University Mathematics Journal, 64(1), 21-54. https://doi.org/10.1512/iumj.2015.64.5469
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