相关论文: The Mobius-Pompeiu metric property

This thesis covers several developments performed in metric-affine gravity. This alternative framework extends General Relativity by considering a more general connection than the one induced by the metric (i.e., arbitrary torsion and…

Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.

We show that the metric universal cover of a plane with a puncture yields an example of a nonstandard hull properly containing the metric completion of a metric space. As mentioned by do Carmo, a nonextendible Riemannian manifold can be…

We consider a natural way of extending the Lebesgue covering dimension to various classes of infinite dimensional separable metric spaces.

The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…

In this paper we introduce the concept of polynomial diagrams and its area for special polynomials.We study the properties of polynomial area diagrams. The formula for the area of an arbitrary polynomial diagram.

A metric space has the universal Lipschitz extension property if for each subspace S embedded quasi-isometrically into an arbitrary metric space M there exists a continuous linear extension of Banach-valued Lipschitz functions on S to those…

We introduce an analog of the Kobayashi-Royden metric on a Riemannian manifold and study its basic properties.

We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…

We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…

This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\R$ that are…

In this paper, we introduce a new type of coupled fixed point theorem in partially ordered complete metric space. We give an example to support of our result.

A quick overview is provided on the current development of the WP metric geometry.

We define metrics on Culler-Vogtmann space, which are an analogue of the Teichmuller metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate…

This note provides an overview of the notion of observable within the setting of multisymplectic geometry. We essentially follow the ideas described by F. H\'elein and J. Kouneiher [17] [18] [19] and in particular in keeping with the…

We state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail the linear algebra…

We explore the relationship in metric spaces between different properties related to the Besicovitch covering theorem, and also consider weak versions of doubling, in connection to the non-uniqueness of centers and radii in arbitrary metric…

Metrics in Grassmannians, or distances between subspaces of same dimension, have many uses, and extending them to the Total Grassmannian of subspaces of different dimensions is an important problem, as usual extensions lack good properties…

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

In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…