Annales AcademiŠ Scientiarum FennicŠ
Mathematica
Volumen 35, 2010, 235-254

SUFFICIENT AND NECESSARY CONDITIONS FOR CONFORMALITY. PART II. ANALYTIC VIEWPOINT

Melkana A. Brakalova

Fordham University, Department of Mathematics
Bronx, New York 10543, U.S.A.; brakalova 'at' fordham.edu

Abstract. This is the second of two papers devoted to the topic of conformality at a point and related notions in the plane. We derive representation formulas and estimates for the modules of families of curves that are images of circles, radial segments and arcs of spirals under a \mu-homeomorphism. We use them to convert the extremal-length type sufficient and necessary conditions for conformality at a point from Part I to analytic sufficient conditions, that depend on directional dilatations and bypass the assumption of K-quaisconformality. Our results extend the TeichmŘller-Wittich-Belinskii theorem, results of Reich and Walczak, the author and Jenkins, and Gutlyanskii and Martio.

2000 Mathematics Subject Classification: Primary 30C62, 30C99.

Key words: Conformality at a point, Beltrami equation, quasiconformal mapping, degenerate Beltrami equation, \mu-homeomorphism, directional dilatation.

Reference to this article: M.A. Brakalova: Sufficient and necessary conditions for conformality. Part II. Analytic viewpoint. Ann. Acad. Sci. Fenn. Math. 35 (2010), 235-254.

Full document as PDF file

doi:10.5186/aasfm.2010.3514

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