Related papers: Extraordinary dimension of maps
Using the notion of modulus of continuity at a point of a mapping between metric spaces, we introduce the notion of extensively bounded mappings generalizing that of Lipschitz mappings. We also introduce a metric on it which becomes a norm…
We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…
We show that expansive maps from a dense subset of a compact metric space into the metric space itself are isometries
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…
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 main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
We give a short proof that there exists a countable state Bernoulli measure maximizing the dimension of their images under the continued fraction expansion.
A smooth map between smooth manifolds is called a special generic map if it has only definite fold points as its singularities. In this paper, we give conditions for a special generic map into the 3-dimensional Euclidean space to be…
We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies…
Positive bi-linear maps between matrix algebras play important roles to detect tri-partite entanglement by the duality between bi-linear maps and tri-tensor products. We exhibit indecomposable positive bi-linear maps between $2\times 2$…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
We introduce a general definition of almost $p$-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost $p$-summing…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
We prove that a typical Lipschitz mapping between any two Banach spaces is non-differentiable at typical points of any given subset of its domain in the most extreme form. This is a new result even for Lipschitz mappings between Euclidean…
We show that for a metric space with an even number of points there is a 1-Lipschitz map to a tree-like space with the same matching number. This result gives the first basic version of an unoriented Kantorovich duality. The study of the…
We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric…