Quasiregular mappings of maximal local modulus of continuity

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Abstract

We study the behavior of a K-quasiregular mapping near points where its local modulus of continuity has order 1/K. We prove that the mapping is spherically analytic at such points and is asymptotically a rotation on circles. This result is used to prove sharp distortion estimates, including a version of Schwarz's lemma.

Original languageEnglish (US)
Pages (from-to)211-222
Number of pages12
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume29
Issue number1
StatePublished - May 10 2004
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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