Related papers: QCH mappings between unit ball and domain with $C^…

In this article, we consider the H\"{o}lder continuity of injective maps in Orlicz-Sobolev classes defined on the unit ball. Under certain conditions on the growth of dilatations, we obtain the H\"{o}lder continuity of the indicated class…

Teichm\"uller's classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself, and maps a given…

For an harmonic map $u$ from a domain $U\subset{\rm X}$ in an ${\sf RCD}(K,N)$ space ${\rm X}$ to a ${\sf CAT}(0)$ space ${\rm Y}$ we prove the Lipschitz estimate \[ {\rm Lip}(u|_B)\leq \frac {C(K^-R^2,N)}r\inf_{{\sf o}\in {\rm…

We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains…

In this paper, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to H\"older continuous maps on the boundary, with H\"older exponent strictly greater than 1/2.

The purpose of this article is to study Lipschitz CR mappings from an $h$-extendible (or semi-regular) hypersurface in $\mbb C^n$. Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A…

Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2, that $D\subset E$ and $D'\subset E'$ are domains, and that $f: D\to D'$ is a homeomorphism. In this paper, we prove that if there exists some constant $M>1$…

In this note we show that gradient of Harmonic functions on a smooth domain with Lipschitz boundary values is pointwise bounded by a universal function which is in $L^p$ for all finite $p\geq 1$.

We show that if a bounded domain in complex Euclidean space with $\mathcal{C}^{1,1}$ boundary covers a compact manifold, then the domain is biholomorphic to the unit ball.

We find conditions for a smooth nonlinear map $f:U\rightarrow V$ between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some $c$ and each positive $\varepsilon<c$ the image $% f(B_\varepsilon(x))$ of…

It is proved the following theorem, if $w$ is a quasiconformal harmonic mappings between two Riemann surfaces with smooth boundary and aproximate analytic metric, then $w$ is a quasi-isometry with respect to Euclidean metric.

We study classes of domains in $\mathbb{R}^{d+1},\ d \geq 2$ with sufficiently flat boundaries that admit a decomposition or covering of bounded overlap by Lipschitz graph domains with controlled total surface area. This study is motivated…

In this note, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to $\mathcal{C}^2$-smooth maps on the boundary.

In this paper, we investigate the geometric properties of complex-valued pluriharmonic mappings defined over convex Reinhardt domains in $\mathbb{C}^n$. We first establish a multidimensional analogue of the Noshiro-Warschawski Theorem,…

We consider the projectivization of Minkowski space with the analytic continuation of the hyperbolic metric and call this an extended hyperbolic space. We can measure the volume of a domain lying across the boundary of the hyperbolic space…

This paper focuses on properties of \partial-biLipschitz mappings which were recently introduced by Bulter. We establish several characterizations for the class of \partial-biLipschitz mappings between domains in quasiconvex metric spaces.…

We characterize pairs of bounded Reinhardt domains in $\CC^2$ between which there exists a proper holomorphic map and find all proper maps that are not elementary algebraic.

We prove that every quasicontinuous domain that fails to be quasialgebraic admits the unit interval [0, 1] as its monotone Lawson-continuous image. As a result, every countable quasicontinuous domain is quasialgebraic.

We prove the local Lipschitz continuity of sub-elliptic harmonic maps between certain singular spaces, more specifically from the $n$-dimensional Heisenberg group into $CAT(0)$ spaces. Our main theorem establishes that these maps have the…

In the present paper, homeomorphisms in metric spaces which generalize quasiconformal mappings, are investigated. It is proved that, at some conditions on metric spaces and boundaries of corresponding domains, families of above mappings are…