Communications in Mathematical Analysis

A Characterization of Sub-Riemannian Spaces as Length Dilation Structures Constructed Via Coherent Projections

Marius Buliga

Abstract

We introduce length dilation structures on metric spaces, tempered dilation structures and coherent projections and explore the relations between these objects and the Radon-Nikodym property and Gamma-convergence of length functionals. Then we show that the main properties of sub-riemannian spaces can be obtained from pairs of length dilation structures, the first being a tempered one and the second obtained via a coherent projection. Thus we get an intrinsic, synthetic, axiomatic description of sub-riemannian geometry, which transforms the classical construction of a Carnot-Carathéodory distance on a regular sub-riemannian manifold into a model for this abstract sub-riemannian geometry.

Article information

Source
Commun. Math. Anal., Volume 11, Number 2 (2011), 70-111.

Dates
First available in Project Euclid: 25 February 2011

https://projecteuclid.org/euclid.cma/1298669956

Mathematical Reviews number (MathSciNet)
MR2780883

Zentralblatt MATH identifier
1214.51004

Citation

Buliga, Marius. A Characterization of Sub-Riemannian Spaces as Length Dilation Structures Constructed Via Coherent Projections. Commun. Math. Anal. 11 (2011), no. 2, 70--111. https://projecteuclid.org/euclid.cma/1298669956

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