Displaying similar documents to “Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation”

On the Lifshits Constant for Hyperspaces

K. Leśniak (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.

Spaces of Lipschitz functions on metric spaces

Diethard Pallaschke, Dieter Pumplün (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.

Menger curvature and Lipschitz parametrizations in metric spaces

Immo Hahlomaa (2005)

Fundamenta Mathematicae

Similarity:

We show that pointwise bounds on the Menger curvature imply Lipschitz parametrization for general compact metric spaces. We also give some estimates on the optimal Lipschitz constants of the parametrizing maps for the metric spaces in Ω(ε), the class of bounded metric spaces E such that the maximum angle for every triple in E is at least π/2 + arcsinε. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.