Related papers: Some remarks about metric spaces
We give a few simple methods to geometically describe some polygon and chain-spaces in R^d. They are strong enough to give tables of m-gons and m-chains when m <= 6.
Since the end of the 19th century, and after the works of F. Klein and H. Poincar\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen…
These informal notes deal with some topics related to analysis on metric spaces.
The main aim of this article is to investigate the geometric structures admitting by the G\"{o}del spacetime which produces a new class of semi-Riemannian manifolds (see Theorem 4.1 and Theorem 4.5). We also consider some extension of…
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic…
Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space (other than the octonion hyperbolic plane), and consider the space L(M) of oriented geodesics of M. The space L(M) is…
These pages covers my expository talks during the seminar "Sub-Riemannian geometry and Lie groups" organised by the author and Tudor Ratiu at the Mathematics Department, EPFL, 2001. However, this is the first part of three, in preparation,…
A class of Cantor-type spaces and related geometric structures are discussed.
We conjecture the existence of a simple geometric structure underlying questions of reducibility of parabolically induced representations of reductive p-adic groups.
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
We study metric spaces homeomorphic to a closed oriented manifold from both geometric and analytic perspectives. We show that such spaces (which are sometimes called metric manifolds) admit a non-trivial integral current without boundary,…
This is a very short introduction to hierarchically hyperbolic spaces and groups. It is aimed at non-experts, including anyone who may encounter a group with some similarities to mapping class groups.
In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…
We construct natural Riemannian metrics on Seiberg-Witten moduli spaces and study their geometry.
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
The main purpose of this paper is to introduce and study the primal-proximity spaces. Also, we define two new operators via primal proximity spaces and investigate some of their fundamental properties. In addition, we obtain a new topology,…
We present and study a family of metrics on the space of compact subsets of $R^N$ (that we call ``shapes''). These metrics are ``geometric'', that is, they are independent of rotation and translation; and these metrics enjoy many…
In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…