Multiplicity and boundary behavior of quasiregular maps

Antti Rasila

doi:10.1007/s00209-005-0768-y

Multiplicity and boundary behavior of quasiregular maps

Antti Rasila^*

^*Corresponding author for this work

Mathematics with Computer Science

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	611-640
Number of pages	30
Journal	Mathematische Zeitschrift
Volume	250
Issue number	3
DOIs	https://doi.org/10.1007/s00209-005-0768-y
State	Published - Jul 2005

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abstract = "We study the boundary behavior of a bounded quasiregular mapping f: G→ ℝ n . In the main results, Lindel{\"o}f-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.",

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AB - 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.

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