相关论文: Some remarks about metric spaces

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

Basic properties of Hausdorff content, dimension, and measure of subsets of metric spaces are discussed, especially in connection with Lipschitz mappings and topological dimension.

This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds complete with pictures of key examples and a discussion of the properties associated with each notion. We begin with a description of three extrinsic…

Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…

This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.

These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the background material. It starts with the definition of Riemannian…

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a…

In this paper, we offer a brief introduction to the $p$-adic numbers and operations in the metric space defined under the $p$-adic norm. Specifically, we provide a clear description of the derivation of the $p$-adic number via the…

The first papers on o-minimal structures appeared in the mid 1980s, since then the subject has grown into a wide ranging generalisation of semialgebraic, subanalytic and subpfaffian geometry. In these notes we try to show that this is in…

A natural metric on the space of all almost hermitian structures on a given manifold is investigated.

The purpose of this note is to discuss examples of geometric transition from hyperbolic structures to half-pipe and Anti-de Sitter structures in dimensions two, three and four. As a warm-up, explicit examples of transition to Euclidean and…

In this survey, we give an introduction to nearly K\"ahler geometry, and list some results on submanifolds of these spaces. This survey tries by no means to be complete.

The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.

An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…

We introduce the notion of tiling spaces for metric spaces. The class of tiling spaces contains the Euclidean spaces, the middle-third Cantor set, and various self-similar spaces appearing in fractal geometry. For doubling tiling spaces, we…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…

The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.

The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…

We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.