Related papers: Quasicircles and Bounded Turning Circles Modulo bi…

In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure supporting a p-Poincar\'e inequality we show that quasiopen and…

We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show…

We mainly investigate some properties of quasiconformal mappings between smooth 2-dimensional surfaces with boundary in the Euclidean space, satisfying certain partial differential equations (inequalities) concerning Laplacian, and in…

We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct $\ell_1$-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free spaces over…

We introduce a class of metrics on $\mathbb{R}^n$ generalizing the classical Grushin plane. These are length metrics defined by the line element $ds = d_E(\cdot,Y)^{-\beta}ds_E$ for a closed nonempty subset $Y \subset \mathbb{R}^n$ and…

The notion of bounded ideals is introduced for quasi-metric spaces. Such ideals give rise to a monad, the bounded ideal monad, on the category of quasi-metric spaces and non-expansive maps. Algebras of this monad are metric version of local…

The main purpose of the present paper is to define and study the notion of quasi bi-slant submanifolds of almost contact metric manifolds. We mainly concerned with quasi bi-slant submanifolds of cosymplectic manifolds as a generalization of…

We study, for the first time, the maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point of each modulus. Blumenthal showed that for entire maps these sets are…

A natural quantity that measures how well a map $f:\mathbb{R}^{d}\rightarrow \mathbb{R}^{D}$ is approximated by an affine transformation is…

We study the interior and exterior moduli of polygonal quadrilaterals. The main result is a formula for a conformal mapping of the upper half plane onto the exterior of a convex polygonal quadrilateral. We prove this by a careful analysis…

We show that for every $k\ge 3$ there exist complex algebraic cones of dimension $k$ with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they have different degrees. We also prove that homeomorphic…

The main purpose of the note is to explore the invariant properties of sphericalization and flattening and their applications in quasi-metric spaces. We show that sphericalization and flattening procedures on a quasimetric spaces preserving…

We study moduli spaces of twisted quasimaps to a hypertoric variety $X$, arising as the Higgs branch of an abelian supersymmetric gauge theory in three dimensions. These parametrise general quiver representations whose building blocks are…

Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. We show that every homogeneous quasi-morphism on the identity component $Diff_0(M,vol)$ of the group of volume preserving…

We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.

We revisit and generalize the application of a method introduced by Latr\'emoli\`ere and Packer for constructing finitely generated projective modules over the noncommutative solenoid C*-algebras. By realizing them as direct limits of…

Relying on rays, we search for submodules of a module V over a supertropical semiring on which a given anisotropic quadratic form is quasilinear. Rays are classes of a certain equivalence relation on V, that carry a notion of convexity,…

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to defined the notion of quasi $z^\circ$-submodules of M as an extension of $z^\circ$-ideals of R and obtained some related results when M is a…

We provide new conditions that ensure that two metric measure spaces are not quasiconformally equivalent. As an application we deduce that there exists no quasiconformal map between the sub-Riemannian Heisenberg and roto-translation groups.

We introduce a higher dimensional quasiregular map analogous to the trigonometric functions and we use the dynamics of this map to define, for d>1, a partition of d-dimensional Euclidean space into curves tending to infinity such that two…