Results 1 to 10 of about 276,042 (44)

Sub-Riemannian geometry and Lie groups. Part II. Curvature of metric spaces, coadjoint orbits and associated representations [PDF]

arXiv, 2004
This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at http://arxiv.org/abs/math.MG/0210189, and "Tangent bundles to sub-Riemannian groups", math.MG/0307342, available at http://arxiv.org/abs ...
arxiv  

Total orders on compact metric spaces and covering dimension [PDF]

arXiv, 2022
We prove that for a compact metric space the property of having finite covering dimension is equivalent to the existence of a total order with finite snake number.
arxiv  

Quasi-metric and metric spaces [PDF]

arXiv, 2006
We give a short review of a construction of Frink to obtain a metric space from a quasi-metric space. By an example we illustrate the limits of the construction.
arxiv  

Trimming of finite metric spaces [PDF]

arXiv, 2016
We define a class of trim metric spaces and show that every finite metric space is the leaf space of a metric forest with trim base.
arxiv  

An introduction to the geometry of metric spaces [PDF]

arXiv, 2007
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
arxiv  

Another introduction to the geometry of metric spaces [PDF]

arXiv, 2007
Here Lipschitz conditions are used as a primary tool, for studying curves in metric spaces in particular.
arxiv  

Elementary aspects of the geometry of metric spaces [PDF]

arXiv, 2007
The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.
arxiv  

Differentiable structures on metric measure spaces: A Primer [PDF]

arXiv, 2011
This is an exposition of the theory of differentiable structures on metric measures spaces, in the sense of Cheeger and Keith.
arxiv  

Intrinsic L_p metrics for convex bodies [PDF]

arXiv, 2003
Intrinsic $L_p$ metrics are defined and shown to satisfy a dimension--free bound with respect to the Hausdorff metric.
arxiv  

The Maximal Generalised Roundness Of Finite Metric Spaces [PDF]

arXiv, 2020
We provide two simplifications of Sanchez's formula for the maximum generalised roundness of a finite metric space.
arxiv