Assouad dimension, Nagata dimension, and uniformly close metric tangents

Autor:	Donne, Enrico Le, Rajala, Tapio
Rok vydání:	2013
Předmět:	Mathematics - Metric Geometry Mathematics - Geometric Topology 54F45 (Primary) 53C23 54E35 53C17 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 27 pages, 1 figure. To appear on Indiana University Mathematics Journal
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1306.5859 Zobrazit plný text záznamu View this record from Arxiv