Related papers: A new characterization of the mappings of bounded …
We prove a characterization for BLD-mappings between locally complete locally compact path-metric spaces. As a corollary we obtain a sharp limit theorem for BLD-mappings.
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…
In this paper, we first establish two versions of Landau-Bloch type theorem for $(K,K')$-elliptic harmonic mappings with a bounded minimum distortion. Next, we provide several coefficient estimates and a conjecture for $(K,K')$-elliptic…
For mappings of finite distortion actively investigated last 15--20 years, problems of a so-called lower order are discussed. It is proved that, mappings with finite length distortion $f:D\rightarrow {\Bbb R}^n,$ $n\ge 2,$ which have…
In this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance. Nonlinear versions of the corresponding results are also presented.
We consider mappings satisfying a certain estimate of the distortion of the modulus of families of paths, similar to the geometric definition of quasiconformal mappings. Under appropriate restrictions, we show that the class of such…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
We provide a self-contained proof to so-called Martio's conjecture in the class of mappings of bounded length distortion. Unlike the earlier proofs, our proof is not based on the modulus of continuity estimate of Martio from 1970.
When finding an original proof to a known result describing expansive mappings on compact metric spaces as surjective isometries, we reveal that relaxing the condition of compactness to total boundedness preserves the isometry property and…
A behavior of one class of mappings with finite distortion at a neighborhood of the origin is investigated. There is proved a lower estimate of distortion of a distance under mappings mentioned above.
We show that every $L$-BLD-mapping in a domain of $\mathbb{R}^n$ is a local homeomorphism if $L < \sqrt{2}$ or $K_I(f) < 2$. These bounds are sharp as shown by a winding map.
We give an example illustrating that two notions of bounded distortion for $\mathcal C^1$ expanding maps in $\R$ are different.
There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some…
We define a Newman property for BLD-mappings and study its connections to the porosity of the branch set in the setting of generalized manifolds equipped with complete path metrics.
The definition of Linear Symmetry-Based Disentanglement (LSBD) proposed by (Higgins et al., 2018) outlines the properties that should characterize a disentangled representation that captures the symmetries of data. However, it is not clear…
A conserved cosmological perturbation is associated with each quantity whose local evolution is determined entirely by the local expansion of the Universe. It may be defined as the appropriately normalised perturbation of the quantity,…
Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and…
Linear maps preserving pure states of a quantum system of any dimension are characterized. This is then used to establish a structure theorem for linear maps that preserve separable pure states in multipartite systems. As an application, a…
It is established a continuous boundary extension of some class of mappings. Under some additional conditions, we have established that this extension is light in the closure of the definition domain. Under some stronger conditions, we also…
We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group.…