Related papers: On Koebe's theorem for mappings with integral cons…
We prove the validity of the $p$-Brunn-Minkowski inequality for the intrinsic volume $V_k$, $k=2,\dots, n-1$, of convex bodies in $\mathbb{R}^n$, in a neighborhood of the unit ball, for $0\le p<1$. We also prove that this inequality does…
We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the role of the (Lorentzian) modulus of its differential. It is…
We prove a one-parameter family of sharp integral inequalities for functions on the $n$-dimensional unit ball. The inequalities are conformally invariant, and the sharp constants are attained for functions that are equivalent to a constant…
In this work we study the variational problem associated to dimer models, a class of models from integrable probability and statistical mechanics in dimension two which have been the focus of intense research efforts over the last decades.…
The paper is devoted to the study of mappings satisfying the inverse Poletsky inequality. We study the local behavior of these mappings, moreover, we are most interested in the case when the corresponding majorant is integrable on some set…
We study compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces with variable exponents on both bounded and unbounded metric measure spaces. We establish sufficient conditions for compactness, and under additional assumptions, we…
In this paper, we prove a Sanov-type large deviation principle for the sequence of empirical measures of vectors chosen uniformly at random from an Orlicz ball. From this level-$2$ large deviation result, in a combination with Gibbs…
We prove a characterization result in the spirit of the Kinderlehrer-Pedregal Theorem for Young measures generated by gradients of Sobolev maps satisfying the orientation-preserving constraint, that is the pointwise Jacobian is positive…
We establish a version of the Pommerenke-Levin-Yoccoz inequality for the modulus of a polynomial-like restriction of a global polynomial and give two applications. First it is shown that if the modulus of a polynomial-like restriction of an…
We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…
The present paper is devoted to the study of space mappings, which are more general than quasiregular. The analogue of the known V\"ais\"al\"a inequality for the special types of curves was proved for the open, discrete, differentiable a.e.…
Let $D$ be a bounded domain in a complex Banach space. According to the Earle-Hamilton fixed point theorem, if a holomorphic mapping $F : D \mapsto D$ maps $D$ strictly into itself, then it has a unique fixed point and its iterates converge…
A paper is devoted to study of local behavior of so-called $Q$-mappings including qua\-si\-con\-for\-mal mappings and mappings with bounded distortion. It is showed that, such mappings have removable isolated singularities whenever the grow…
This note aims to study the iteration theory of noncommutative self-maps of bounded matrix convex domains. We prove a version of the Denjoy-Wolff theorem for the row ball and the maximal quantization of the unit ball of $\mathbb{C}^d$. For…
For any integer $ p \geq 2 $, we construct a compact Riemannian manifold $ \mathcal{N} $ such that if $ \dim \mathcal{M} > p $, there is a map in the Sobolev space of mappings $ W^{1,p} (\mathcal{M}, \mathcal{N})$ which is not a weak limit…
Recently Gigli developed a Sobolev calculus on non-smooth spaces using module theory. In this paper it is shown that his theory fits nicely into the theory of differentiability spaces initiated by Cheeger, Keith and others. A relaxation…
We re-confirm, for the case of the unit p-ball of R^n, one of recent conjectures of G.Kuperberg on centrally symmetric convex bodies.This conjecture was very recently confirmrd for this particular case by D.A.Gutierrez using polygamma…
In this paper, we investigate the properties of hyperbolic harmonic mappings in the unit ball $\mathbb{B}^{n}$ in $\IR^n$ $(n\geq 2)$. Firstly, we establish necessary and sufficient conditions for a hyperbolic harmonic mapping to be in the…
The paper is devoted to the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact setting is mostly similar to the reversible case developed by…
A new intrinsic volume metric is introduced for the class of convex bodies in $\mathbb{R}^n$. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes…