Related papers: An `almost all versus no' dichotomy in homogeneous…

In this paper we study almost proximal extensions of minimal flows. Let $\pi: (X,T)\rightarrow (Y,T)$ be an extension of minimal flows. $\pi$ is called an almost proximal extension if there is some $N \in \mathbb{N}$ such that the…

We prove new quantitative Schmidt-type theorem for Diophantine approximations with restraint denominators on fractals (more precisely, on $M_0$-sets). Our theorems introduce a sharp balance condition between the growth rate of the sequence…

We generalise M. M. Skriganov's notion of weak admissibility for lattices to include standard lattices occurring in Diophantine approximation and algebraic number theory, and we prove estimates for the number of lattice points in sets such…

A kinetics built upon $q$-calculus, the calculus of discrete dilatations, is shown to describe diffusion on a hierarchical lattice. The only observable on this ultrametric space is the "quasi-position" whose eigenvalues are the levels of…

We survey the theory of locally homogeneous almost-Hermitian spaces. In particular, by using the framework of varying Lie brackets, we write formulas for the curvature of all the Gauduchon connections and we provide explicit examples of…

Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic…

We consider locally symmetric manifolds with a fixed universal covering, and construct for each such manifold M a simplicial complex R whose size is proportional to the volume of M. When M is non-compact, R is homotopically equivalent to M,…

We give a rigorous account and prove continuity properties for the correspondence between almost flat bundles on a triangularizable compact connected space and the quasi-representations of its fundamental group. For a discrete countable…

The aim of this article is to complete results of [M.00] and [B.08] and to show that they imply a rather general existence theorem for meromorphic quotient of strongly quasi-proper meromorphic equivalence relations. In this context, generic…

Via multilinear algebra, we formulate a criterion for connectedness in the parametric geometry of numbers in terms of pencils, which are certain algebraic varieties in the space of matrices. As a consequence, we obtain a connectedness…

The paper is devoted to perfect and almost perfect homogeneous polytopes in Euclidean spaces. We classified perfect and almost perfect polytopes among all regular polytopes and all semiregular polytopes excepting Archimedean solids and two…

It is an old conjecture, that finite $H$-spaces are homotopy equivalent to manifolds. Here we prove that this conjecture is true for loop spaces. Actually, we show that every quasi finite loop space is equivalent to a stably parallelizable…

Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…

For a given null-cobordant Riemannian $n$-manifold, how does the minimal geometric complexity of a null-cobordism depend on the geometric complexity of the manifold? In [Gro99], Gromov conjectured that this dependence should be linear. We…

Let $F \subseteq [0,1]$ be a set that supports a probability measure $\mu$ with the property that $ |\widehat{\mu}(t)| \ll (\log |t|)^{-A}$ for some constant $ A > 0 $. Let $\mathcal{A}= (q_n)_{n\in \mathbb{N}} $ be a sequence of natural…

We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.

We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…

The main goal of this note is to develop a metrical theory of Diophantine approximation within the framework of the de Mathan-Teulie Conjecture, also known as the `Mixed Littlewood Conjecture'. Let p be a prime. A consequence of our main…

Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of…

Let $Y\subset{\mathbb R}^n$ be a triangulable set and let $r$ be either a positive integer or $r=\infty$. We say that $Y$ is a $\mathscr{C}^r$-approximation target space, or a $\mathscr{C}^r\text{-}\mathtt{ats}$ for short, if it has the…