Related papers: Linear measure and $K$-quasiconformal harmonic map…
Differential logical relations are a method to measure distances between higher-order programs. They differ from standard methods based on program metrics in that differences between functional programs are themselves functions, relating…
In this paper, we investigate the relationship between semisolidity and locally weak quasisymmetry of homeomorphisms in quasiconvex and complete metric spaces. Our main objectives are to (1) generalize the main result in [X. Huang and J.…
Consider a mapping $f\colon X\to Y$ between two metric measure spaces. We study generalized versions of the local Lipschitz number $\mathrm{Lip} f$, as well as of the distortion number $H_f$ that is used to define quasiconformal mappings.…
We study non-linear functionals, including quasi-linear functionals, p-conic quasi-linear functionals, d-functionals, r-functionals, and their relationships to deficient topological measures and topological measures on locally compact…
We study complex non-K\"ahler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed…
Harmonic mappings into Teichmuller spaces appear in the study of manifolds which are fibrations whose fibers are Riemann surfaces. In this article we will study the existence and uniquenesses questions of harmonic mappings into Teichmuller…
The present paper is devoted to the study of mappings with finite distortion on Riemannian manifolds. Theorems on local behavior of generalized quasiisometries with unbounded characteristic of quasiconformality are obtained.
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, logarithmic means, etc. Inequalities involving logarithmic mean with differences among other means are presented
We review and compare several measures that identify quantum states that are "macroscopically quantum". These measures were initially formulated either for photonic systems or spin ensembles. Here, we compare them through a simple model…
Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…
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…
The primary objective of this paper is to establish several sharp versions of improved Bohr inequalities, refined Bohr inequalities, and Bohr-Rogosinski inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings…
Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this paper, we study two questions in this setting. The first is to show that…
This paper presents a general existence and uniqueness result for harmonic maps with prescribed singularities into non-positively curved targets, and surveys a number of applications to general relativity. It is based on a talk delivered by…
The purpose of this paper is twofold. First, we establish several sharp Hardy-Littlewood type radial growth theorems for harmonic $(K,K')$-quasiregular mappings. Second, we prove some sharp coefficient growth theorems for such mappings. In…
This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of $n$ positive real numbers. Together with this interpretation, we prove some relevant properties that…
We prove that the distortion function of the Gauss map of a harmonic surface coincides with the distortion function of the surface. Consequently, Gauss map of a harmonic surface is ${\mathcal{K}}$ quasiregular if and only if the surface is…
We consider in this paper the quantum limits for measurements on macroscopic bodies which are obtained in a novel way employing the concept of decoherence coming from an analysis of the quantum mechanics of dissipative systems. Two cases…
This article is a survey of results involving conformal deformation of Riemannian metrics and fully nonlinear equations.
We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent…