Related papers: On injectivity of quasiregular mappings
We generalize the classical K\"onig's and B\"ottcher's Theorems in complex dynamics to certain quasiregular mappings in the plane. Our approach to these results is unified in the sense that it does not depend on the local injectivity, or…
The paper is devoted to the study of mappings with non--bounded characteristics of quasiconformality. The analog of the theorem about radius injectivity of locally quasiconformal mappings was proved for some class of mappings. There are…
Establishing that a demand mapping is injective is core first step for a variety of methodologies. When a version of the law of demand holds, global injectivity can be checked by seeing whether the demand mapping is constant over any line…
We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.
It is stated a series of criteria of equicontinuity and normality for classes of space mappings with integral restrictions. It is shown that the found conditions are not only sufficient but also necessary. It is given applications to…
We prove that an injection from the integer set into the real line admits a quasiconformal extension to the complex plane if and only if it is quasisymmetric.
We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including…
We discuss the issue of branching in quasiregular mapping, and in particular the relation between branching and the problem of finding geometric parametrizations for topological manifolds. Other recent progress and open problems of a more…
This paper introduces three sets of sufficient conditions, for generating bijective simplicial mappings of manifold meshes. A necessary condition for a simplicial mapping of a mesh to be injective is that it either maintains the orientation…
We prove a far-reaching generalization of Rickman's Picard theorem for a surprisingly large class of mappings, based on the recently developed theory of quasiregular values. Our results are new even in the planar case.
We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement of a result that gives bounds on the distortion…
We consider quasiconformal mappings of the unit disk that have a planar extension which have $p$-integrable distortion. In this paper, we establish a bound for the modulus of continuity for the inverse mapping and show sharpness of this…
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…
A behavior of open discrete mappings, which are quasiconformal in the mean, is investigated. It is proved that the classes of mappings mentioned above are equicontinuous (normal).
We study, for the first time, the maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point of each modulus. Blumenthal showed that for entire maps these sets are…
We prove that if a non-singular planar map $\Lambda \in C^2(R^2,R^2)$ has a convex component, then $\Lambda$ is injective. We do not assume strict convexity.
We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
We survey the recent developments in the theory of quasireg- ular mappings in metric spaces. In particular, we study the geometric porosity of the branch set of quasiregular mappings in general metric measure spaces, and then, introduce the…
This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…