Assouad Dimension, Nagata Dimension, and Uniformly Close Metric Tangents
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
Julkaistu sarjassa
Indiana University Mathematics JournalPäivämäärä
2015Tekijänoikeudet
© Indiana University Mathematics Journal. Published in this repository with the kind permission of the publisher.
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.
Julkaisija
Indiana UniversityISSN Hae Julkaisufoorumista
0022-2518Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/24611622
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