Related papers: On the inverse Poletsky inequality with cotangent …

We consider the complex case of the so-called S-inequality. It concerns the behaviour of the Gaussian measures of dilations of convex and rotationally symmetric sets in C^n (rotational symmetry is invariance under the multiplication by…

A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…

Let k be an algebraically closed field of characteristic p>0 and let G be a symplectic or general linear group over k. We consider induced modules for G under the assumption that p is bigger than the greatest hook length in the partitions…

We define finite distortion $\omega$-curves and we show that for some forms $\omega$ and when the distortion function is sufficiently exponentially integrable the map is continuous, differentiable almost everywhere and has Lusin's (N)…

Dilatation, i.e. scale, symmetry in the presence of the dilaton in Minkowski space is derived from diffeomorphism symmetry in curved spacetime, incorporating the volume-preserving diffeomorphisms. The conditions for scale invariance are…

We prove an inequality related to arctanh, resolving a conjecture of Gu and Polyanskiy [arXiv:2303.14689].

In the Orlicz type spaces ${\mathcal S}_{M}$, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of…

This is a continuation of our previous work 0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity…

A theorem of Kaplansky asserts that a semigroup of matrices with entries from a field whose members all have singleton spectra is triangularizable. Indeed, Kaplansky's Theorem unifies well-known theorems of Kolchin and Levitzki on…

In these notes, we present versions of trace theorems for Sobolev spaces over an interval in the real line, and also a one-dimensional version of the well-known Poincare inequality.

In this paper we give a general family of conformal invariants associated to bordered Riemann surfaces endowed with boundary parametrizations, or equivalently compact surfaces endowed with conformal maps. Each invariant is specified by a…

Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular…

This article is devoted to inverse problems for nonlinear equations of the modified transfer, which can be regarded as a manageable problem. Various productions such problems for normal (unmodified) of the transport equation studied earlier…

This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges,…

We derive transport-entropy inequalities for mixed binomial point processes, and for Poisson point processes. We show that when the finite intensity measure satisfies a Talagrand transport inequality, the law of the point process also…

We establish various Hardy-type inequalities for the Dirichlet Laplacian in perturbed periodically twisted tubes of non-circular cross-sections. We also state conjectures about the existence of such inequalities in more general regimes,…

Drazin inverses are a special kind of generalized inverses that can be defined for endomorphisms in any category. A natural question to ask is whether one can somehow extend the notion of Drazin inverse to arbitrary maps - not simply…

We prove boundary inequalities in arbitrary bounded Lipschitz domains on the trace space of Sobolev spaces. For that, we make use of the trace operator, its Moore-Penrose inverse, and of a special inner product. We show that our trace…

We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincar\'e…

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.…