相关论文: The Mobius-Pompeiu metric property

We study the Bishop-Phelps-Bollobas property for numerical radius within the framework of C(K) spaces. We present several sufficient conditions on a compact space K ensuring that C(K) has the Bishop-Phelps-Bollobas property for numerical…

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face is to find the discrete protoforms of…

For any countable $CW$-complex $K$ and a cardinal number $\tau\geq\omega$ we construct a completely metrizable space $X(K,\tau)$ of weight $\tau$ with the following properties: $\e X(K,\tau)\leq K$, $X(K,\tau)$ is an absolute extensor for…

A Moebius structure (on a set X) is a class of metrics having the same cross-ratios. A Moebius structure is ptolemaic if it is invariant under inversion operations. The boundary at infinity of a CAT(-1) space is in a natural way a Moebius…

We prove a bumpy metric theorem in the sense of Ma\~{n}e for non-convex Hamiltonians that are satisfying a certain geometric property.

This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…

Typical properties of measure space automorphisms with respect to the Halmos and Alpern-Tikhonov metrics are discussed.

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

In this paper geometry of Gromov-Hausdorff distance on the class of all metric spaces considered up to an isometry is investigated. For this class continuous curves and their lengths are defined, and it is shown that the Gromov-Hausdorff…

We give a short introduction to the theory of modular metric spaces. This is a corrected version of the paper [1], which had some errors. We are grateful to V. V. Chistyakov for bringing these to our attention.

In this paper, we consider boundary extensions of two classes of mappings between metric measure spaces. These two mapping classes extend in particular the well-studied geometric mappings such as quasiregular mappings with integrable…

The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…

We study the geometrical properties of the utility space (the space of expected utilities over a finite set of options), which is commonly used to model the preferences of an agent in a situation of uncertainty. We focus on the case where…

Projective metrics on vector spaces over finite fields, introduced by Gabidulin and Simonis in 1997, generalize classical metrics in coding theory like the Hamming metric, rank metric, and combinatorial metrics. While these specific metrics…

We establish some geometrical properties of the space of idempotent probability measures. In particular, for a compact $X$ it is established that if the space $I_{3}(X)\backslash X$ is hereditary normally, then $X$ is metrizable; some…

We introduce the notion of topological hyperbolicity to characterize the largeness of the topological fundamental group of a complex variety. Inspired by the Shafarevich conjecture, we propose to study the topological hyperbolicity of…

In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and…

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

In this note, we highlight some properties of the metric projection onto a closed convex in a Hilbert space. In particular, we use some recent results on fixed points of nonexpansive potential operators.

Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In…