Related papers: Another introduction to the geometry of metric spa…
Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
These are some basic notes concerning Holder and Lipschitz classes on metric spaces.
Some examples and basic properties of ultrametric spaces are briefly discussed.
These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.
These notes deal with metric spaces, Hausdorff measures and dimensions, Lipschitz mappings, and related topics. The reader is assumed to have some familiarity with basic analysis, which is also reviewed.
It is proved that a parameterized curve in a metric space $X$ is absolutely continuous if and only if its composition with any Lipschitz function on $X$ is absolutely continuous.
The standard arithmetic measures of center, the mean and median, have natural topological counterparts which have been widely used in continuum theory. In the context of metric spaces it is natural to consider the Lipschitz continuous…
We prove the equivalence of two seemingly very different ways of generalising Rademacher's theorem to metric measure spaces. One such generalisation is based upon the notion of forming partial derivatives along a very rich structure of…
We study the metric structure of walks on graphs, understood as Lipschitz sequences. To this end, a weighted metric is introduced to handle sequences, enabling the definition of distances between walks based on stepwise vertex distances and…
The triangular ratio metric is studied in subdomains of the complex plane and Euclidean $n$-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the…
Lattices and periodic point sets are well known objects from discrete geometry. They are also used in crystallography as one of the models of atomic structure of periodic crystals. In this paper we study the embedding properties of spaces…
We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the…
The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an…
Let $G \subsetneq \mathbb{R}^n$ be a domain and let $d_1$ and $d_2$ be two metrics on $G$. We compare the geometries defined by the two metrics to each other for several pairs of metrics. The metrics we study include the distance ratio…
The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
In this paper, the Lipschitz clustering property of a metric space refers to the existence of Lipschitz retractions between its finite subset spaces. Obstructions to this property can be either topological or geometric features of the…
Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains a distinguished group, known as the Lipschitz group. We show that only a quotient of this group remains meaningful in…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…