Related papers: Remarks on conformal modulus in metric spaces

We prove that uniformly disconnected subsets of metric measure spaces with controlled geometry (complete, Ahlfors regular, supporting a Poincare inequality, and a mild topological condition) are contained in a quasisymmetric arc. This…

We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out…

For a (compact) subset $K$ of a metric space and $\varepsilon > 0$, the {\em covering number} $N(K , \varepsilon )$ is defined as the smallest number of balls of radius $\varepsilon$ whose union covers $K$. Knowledge of the {\em metric…

We give an alternate proof to the following generalization of the uniformization theorem by Bonk and Kleiner. Any linearly locally connected and Ahlfors 2-regular closed metric surface is quasisymmetrically equivalent to a model surface of…

Let $N$ be a closed, connected, and oriented Riemannian manifold, which admits a quasiregular $\omega$-curve $\mathbb{R}^n \to N$ with infinite energy. We prove that, if the de Rham class of $\omega$ is non-zero and belongs to a so-called…

We consider the problem of classifying quadruples $(K,E,m_1,m_2)$ where $K$ is a number field, $E$ is an elliptic curve defined over $K$ and $(m_1,m_2)$ is a pair of relatively prime positive integers for which the intersection $K(E[m_1])…

We define a measure of noncompactness $\lambda$ on the standard Hilbert $C^*$-module $l^2(\mathcal A)$ over a unital $C^*$-algebra, such that $\lambda(E)=0$ if and only if $E$ is $\mathcal A$-precompact (i.e.\ it is $\varepsilon$-close to a…

This paper first studies the regularity of conformal homeomorphisms on smooth locally embeddable strongly pseudoconvex CR manifolds. Then moduli of curve families are used to estimate the maximal dilatations of quasiconformal…

We develop a global twistor correspondence for pseudo-Riemannian conformal structures of signature (++--) with self-dual Weyl curvature. Near the conformal class of the standard indefinite product metric on S^2 x S^2, there is an…

Given a degeneration of compact projective complex manifolds $X$ over the punctured disc, with meromorphic singularities, and a relatively ample line bundle $L$ on $X$, we study spaces of plurisubharmonic metrics on $L$, with particular…

This paper is concerned with a covering problem of Euclidean space by a particular arrangement of cones that are not necessarily full and are allowed to overlap. The problem provides an equivalent geometric reformulation of the solvability…

We find solutions $E:\Omega\to\mathbb{R}^3$ of the problem \begin{eqnarray*} \left\{ \begin{aligned} &\nabla\times(\mu(x)^{-1}\nabla\times E) - \omega^2\epsilon(x) E = \partial_E F(x,E) &&\quad \text{in }\Omega\\%\newline &\nu\times E = 0…

We study equivariant affine embeddings of homogeneous spaces and their equivariant automorphisms. An example of a quasiaffine, but not affine, homogeneous space with finitely many equivariant automorphisms is presented. We prove the…

We give an example of a planar set $E\subset \mathbb{R}^2$ for which the boundary $\partial E_\varepsilon$ of its $\varepsilon$-neighbourhood $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x, E) \leq \varepsilon \}$ is nowhere…

Let $M$ be a compact nonnegatively curved Riemannian manifold admitting an isometric action by a compact Lie group $\mathsf G$ in a way that the quotient space $M/\mathsf G$ has nonempty boundary. Let $\pi : M \to M/\mathsf G$ denote the…

We study the exact null controllability of a class of non-autonomous conformable fractional semi-linear evolution systems with nonlocal initial conditions in Hilbert spaces. The analysis is carried out within the framework of conformable…

We find necessary and sufficient conditions for a Lipschitz map $f:\mathbb{R}E\to X$, into a metric space to have the image with the $k$-dimensional Hausdorff measure equal zero, $H^k(f(E))=0$. An interesting feature of our approach is that…

We investigate the moduli space ${\mathcal P}_g$ of smooth complex projective curves of genus $g$ equipped with a projective structure. When $g\, \geq\, 3$, it is shown that this moduli space ${\mathcal P}_g$ does not admit any nonconstant…

We show that given a quasi-circle $C$ in $\partial_{\infty}\mathbb{H}^3$ (respectively in $\partial_{\infty} \mathbb{ADS}^3$) and a complete conformal metric $h$ on $\mathbb{D}$ whose curvature $K_h$ takes values in a compact subset of…

We study spaces of conformal blocks associated with line bundles over elliptic curves, with coefficients in a vertex algebra. For vertex algebras satisfying suitable finiteness and semisimplicity conditions, which are met by all admissible…