Related papers: Quasicircles and Bounded Turning Circles Modulo bi…

In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on…

Suppose that $f$ is a $K$-quasiconformal self-mapping of the unit disk $\mathbb{D}$, which satisfies the following: $(1)$ the biharmonic equation $\Delta(\Delta f)=g$ $(g\in \mathcal{C}(\overline{\mathbb{D}}))$, (2) the boundary condition…

We determine the algebraic structure of the multiplicative loops for locally compact $2$-dimensional topological connected quasifields. In particular, our attention turns to multiplicative loops which have either a normal subloop of…

We study locally compact metric spaces that enjoy various forms of homogeneity with respect to M\"obius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with…

In this paper we show that if $Y=N \times \mathbb{Q}_m$ is a metric space where $N$ is a Carnot group endowed with the Carnot-Caratheodory metric then any quasisymmetric map of $Y$ is actually bilipschitz. The key observation is that $Y$ is…

In this paper we study quasiconformal curves which are a special case of quasiregular curves. Namely embeddings $\Omega\rightarrow\mathbb{R}^m$ from some domain $\Omega\subset\mathbb{R}^n$ to $\mathbb{R}^m$, where $n\leq m$, which belong in…

The uniform disconnectedness is an important invariant property under bi-Lipschitz mapping, and the Assouad dimension $\dim _{A}X<1$ implies the uniform disconnectedness of $X$. According to quasi-Lipschitz mapping, we introduce the…

We study various properties of quasimodular forms by using their connections with Jacobi-like forms and pseudodifferential operators. Such connections are made by identifying quasimodular forms for a discrete subgroup $\G$ of $SL(2, \bR)$…

We show that if $f:X\to Y$ is a quasisymmetric mapping between Ahlfors regular spaces, then $\dim_H f(E)\leq\dim_H E$ for "almost every" bounded Ahlfors regular set $E\subseteq X$. If additionally, $X$ and $Y$ are Loewner spaces then…

We study quasiisometries between negatively curved homogeneous manifolds associated with diagonalizable derivations on Heisenberg algebras. We classify these manifolds up to quasiisometry, and show that all quasiisometries between such…

We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling…

We give a proof, based on Lipschitz quotient mappings, for the fact that limits of BLD-mappings between manifolds of bounded geometry are BLD. Furthermore we show that such mappings share some properties of covering maps and especially have…

Given two Ahlfors-David regular sets in metric spaces, we study the question whether one of them has a subset bilipschitz equivalent with the other.

We look at the work of Oleg Ivrii connected with the dimension of quasicircles for asymptotically small quasiconformality parameter $k$. We intend to make this work more easily accessible. Our main focus is the integral means spectrum…

We prove that any metric surface (that is, metric space homeomorphic to a 2-manifold with boundary) with locally finite Hausdorff 2-measure is the Gromov-Hausdorff limit of polyhedral surfaces with controlled geometry. We use this result,…

In this paper, the Lipschitz clustering property of a metric space refers to the existence of Lipschitz retractions between its finite subset spaces. Obstructions to this property can be either topological or geometric features of the…

We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous…

We introduce a moduli space of ``complete quasimaps'' to $\mathsf{Bl}_{\mathbb{P}^s}(\mathbb{P}^r)$. The construction, following previous work for curves on projective spaces, essentially proceeds by blowing up Ciocan-Fontanine--Kim's space…

We establish that every $K$-quasiconformal mapping of $w$ of the unit disk $\ID$ onto a $C^2$-Jordan domain $\Omega$ is Lipschitz provided that $\Delta w\in L^p(\ID)$ for some $p>2$. We also prove that if in this situation $K\to 1$ with…

We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.