Related papers: Quasiregular values and Rickman's Picard theorem
We introduce a general definition of almost $p$-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost $p$-summing…
The increasing application of deep-learning is accompanied by a shift towards highly non-linear statistical models. In terms of their geometry it is natural to identify these models with Riemannian manifolds. The further analysis of the…
We give the algebra of quasimodular forms a collection of Rankin-Cohen operators. These operators extend those defined by Cohen on modular forms and, as for modular forms, the first of them provide a Lie structure on quasimodular forms.…
A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class $\Lambda_*$.…
We introduce a relaxed version of the metric definition of quasiconformality that is natural also for mappings of low regularity, including $W_{\mathrm{loc}}^{1,1}(\mathbb{R}^n;\mathbb{R}^n)$-mappings. Then we show on the plane that this…
The present paper is devoted to the study of classes of mappings with non--bounded characteristics of quasiconformality. It is proved that the normal families of mappings distorting the families of mappings in ${\Bbb R}^n$ by special way,…
In this short note, we consider quasiregular local homeomorphisms on uniform domains. We prove that such mappings always can be extended to some boundary points along John curves, which extends the corresponding result of Rajala [Amer. J.…
We prove that a family of quasiregular mappings of a domain $\Omega$ which are uniformly bounded in $L^p$ for some $p>0$ form a normal family. From this we show how an elliptic estimate on a functional differences implies all directional…
We study the splitting behaviour of quasilinear $p$-forms in the spirit of the theory of nondegenerate quadratic forms over fields of characteristic different from 2 using an analogue of M. Knebusch's generic splitting tower. Several new…
We show that a class of quasiregular Latt\`es maps, called orthotopic Latt\`es maps, are cellular Markov maps. This provides examples of expanding Thurston-type maps that are also uniformly quasiregular, and whose visual metrics are…
Quasiregular mappings $f:\Omega\subset\R^{n}\to \R^{n}$ are a natural generalization of analytic functions from complex analysis and provide a theory which is rich with new phenomena. In this paper we extend a well-known result of A.~Chang…
Let $K\ge 1$. We prove Zygmund theorem for $K-$quasiregular harmonic mappings in the unit disk $\mathbb{D}$ in the complex plane by providing a constant $C(K)$ in the inequality $$\|f\|_{1}\le C(K)(1+\|\mathrm{Re}\,(f)\log^+ |\mathrm{Re}\,…
In this paper, we prove that sufficiently regular solutions of any quasilinear PDE can be approximated by solutions of systems of N distinguishable particles, to within 1/ ln(N ). This intruiguing result is related to recent developments in…
We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasi-homomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping…
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result…
The present paper is devoted to questions located at the junction of the theory of space quasiconformal mappings and Riemannian surfaces. Theorems on local behavior of one class of open discrete mappings with unbounded characteristic of…
In this paper, we establish an improved coefficient bounds for quasiregular and elliptic harmonic mappings and using these bounds we establish Landau-Bloch type theorem for $(K,K')$-elliptic and K-quasiregular harmonic mappings in plane.…
We prove that a harmonic quasiconformal mapping defined on a finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits a quasiconformal extension to the whole plane if its Schwarzian…
Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical…
In this paper we define and study quasipolar general rings (with or without identity) and extend many of the basic results to the wider class. We obtain some new characterizations of quasipolar and strongly $\pi$-regular elements by using…