Algebraic and analytic properties of quasimetric spaces with dilations

Details Algebraic and analytic properties of quasimetric spaces with dilations Algebraic and analytic properties of quasimetric spaces with dilations

2010-05-20

arxiv.org/abs/1005.3640v3

Mathematics

Metric Geometry

To appear in the Proceedings of International Conference on Complex Analysis & Dynamical Systems IV May 18-22, 2009 Nahariya,

Scientific paper

We provide an axiomatic approach to the theory of local tangent cones of regular sub-Riemannian manifolds and the differentiability of mappings between such spaces. This axiomatic approach relies on a notion of a dilation structure which is introduced in the general framework of quasimetric spaces. Considering quasimetrics allows us to cover a general case including, in particular, minimal smoothness assumptions on the vector fields defining the sub-Riemannian structure. It is important to note that the theory existing for metric spaces can not be directly extended to quasimetric spaces.

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