Boundary behavior of quasiregular mappings (original) (raw)

Multiplicity and boundary behavior of quasiregular maps

2005

We study the boundary behavior of a bounded quasiregular mapping f: G? R n. In the main results, Lindelöf-type problems are studied in connection with the local topological index i (x, f). The existence of certain types of limits at a given boundary point b?? G is shown. The assumptions involve local topological index of the mapping f on a given sequence of points approaching the boundary point b.

Angular and approximate limits of quasiregular mappings

2003

Abstract. Concepts of angular and approximate limit are introduced. We give a brief introduction to these and related concepts in the context of quasiregular mappings of Rn. The main goal in the study of this topic is to establish criteria for a quasiregular mapping to have angular and approximate limits at a given boundary point. We prove a version of the Schwarz lemma for quasiregular mappings by using results of P. Järvi, S. Rickman and M. Vuorinen.

On Boundary Correspondence Under Quasiconformal Mappings

1996

We study boundary properties of quasiconformal self-mappings depending on complex dilatations. We give some new conditions for the corresponding quasisymmetric function to be asymptotically symmetric and obtain an explicit asymptotical representation for the distortion ratio of boundary correspondence when the complex dilatation has directional limits.

On the local behaviour of quasi-conformal mappings

Izvestiya: Mathematics, 1995

This paper is devoted to the study of the local behaviour of quasiconformal mappings on the plane and related questions of boundary correspondence in dependence on properties of complex characteristics. The Gardiner-Sullivan symmetries are investigated as well as quasi-circles asymptotically conformal in the sense of Becker and Ponfmerenke.

Analytic sets and the boundary regularity of CR mappings

Proceedings of the American Mathematical Society, 2001

It is shown that if a continuous CR mapping between smooth real analytic hypersurfaces of finite type in C n {\mathbf C}^n extends as an analytic set, then it extends as a holomorphic mapping.

Ju l 2 00 5 BOUNDARY LIMITS FOR BOUNDED QUASIREGULAR MAPPINGS

2005

In this paper we establish results on the existence of nontangential limits for weighted A-harmonic functions in the weighted Sobolev space W 1,q w (B ), for some q > 1 and w in the Muckenhoupt Aq class, where B is the unit ball in R. These results generalize the ones in section §3 of [KMV], where the weight was identically equal to one. Weighted A-harmonic functions are weak solutions of the partial differential equation div(A(x,∇u)) = 0, where α w(x) |ξ| ≤ 〈A(x, ξ), ξ〉 ≤ β w(x) |ξ| for some fixed q ∈ (1,∞), where 0 < α ≤ β < ∞, and w(x) is a q-admissible weight as in Chapter 1 in [HKM]. Later, we apply these results to improve on results of Koskela, Manfredi and Villamor [KMV] and Martio and Srebro [MS] on the existence of radial limits for bounded quasiregular mappings in the unit ball of R with some growth restriction on their multiplicity function. 1991 Mathematics Subject Classification. Primary: 30C65, Secondary: 46E35.