Related papers: Large inductive dimension of the Smirnov remainder

A two-dimensional Minkowski spacetime diagram is neatly represented on a Euclidean ordinary plane. However the Euclidean lengths of the lines on the diagram do not correspond to the true values of physical quantities in spacetime, except…

In this paper, we generalize Dranishnikov's asymptotic inductive dimension to the setting of coarse proximity spaces. We show that in this more general context, the asymptotic inductive dimension of a coarse proximity space is bigger or…

This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.

Compactness is one of the most versatile tools in the analysis of nonlinear PDEs and systems. Usually, compactness is established by means of some embedding theorem between functional spaces. Such theorems, in turn, rely on appropriate…

The purpose of this article is to survey some of the context, achievements, challenges and mysteries of the field of metric dimension reduction, including new perspectives on major older results as well as recent advances.

This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.

In theories which require a space of dimension d>4, there is a natural mechanism of suppressing neutrino masses: while Standard Model fields are confined to a 3-brane, right handed neutrinos live in the bulk. Due to Kaluza-Klein…

We study inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold under dimensional reduction. Stability due to different types of effective potentials is analyzed for specific configurations of…

Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry…

We develop some basic Lipschitz homotopy technique and apply it to manifolds with finite asymptotic dimension. In particular we show that the Higson compactification of a uniformly contractible manifold is mod $p$ acyclic in the finite…

Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications, one usually discretizes the space of smooth curves and…

We compute the Large N limit of several objects related to the two-dimensional Euclidean Yang-Mills measure on compact connected orientable surfaces of genus larger or equal to one, with a structure group taken among the classical groups of…

We use algebraic geometry over pointed monoids to give an intrinsic interpretation for the compactification of the spectrum of the ring of integers of a number field $K$, for the projective line over algebraic extensions of $\mathbb{F}_1$…

The magnitude of metric spaces does not appear to possess a simple, convenient continuity property, and previous studies have presented affirmative results under additional constraints or weaker notions, as well as counterexamples. In this…

This paper explores features of an idealized mathematical machine (algorithm) that would be capable of reconstructing the gravitational nature (the multipolar structure or spacetime metric) of a compact object, by observing gravitational…

In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to…

Smooth deformations of a Minkowski type metric in a four-dimensional space-time manifold are considered. Deformations of the basic spin-tensorial fields associated with this metric are calculated and their application to calculating the…

We prove a sharp logarithmic Sobolev inequality which holds for submanifolds in Euclidean space of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature.

We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane.

We give an elementary proof of a compact embedding theorem in abstract Sobolev spaces. The result is first presented in a general context and later specialized to the case of degenerate Sobolev spaces defined with respect to nonnegative…