Sufficient and necessary conditions for conformality. Part II. Analytic viewpoint
| Autor: | Melkana A. Brakalova |
|---|---|
| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Annales Academiae Scientiarum Fennicae Mathematica. 35:235-254 |
| ISSN: | 1798-2383 1239-629X |
| DOI: | 10.5186/aasfm.2010.3514 |
| Popis: | This paper is dedicated in loving memory to V.V. Alexandrov and A.A. Gol'dberg. 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 mod- ules of families of curves that are images of circles, radial segments and arcs of spirals under a "-homeomorphism. We use them to convert the extremal-length type sucient and necessary con- ditions for conformality at a point from Part I to analytic sucient conditions, that depend on directional dilatations and bypass the assumption of K-quaisconformality. Our results extend the Teichmuller-Wittich-Belinskii theorem, results of Reich and Walczak, the author and Jenkins, and Gutlyanskii and Martio. 1. Definitions and main results Conformality at a point (see (1.3)) and related notions in the plane are rich properties that have had applications in the theory of Riemann surfaces, Nevanlinna theory, in the study of regularity properties of the boundary correspondence, local modulus of continuity properties and others (e.g. (10, 15, 16, 17, 22, 26)). Our main results, Theorems 1.2-1.4, provide sucient |
| Databáze: | OpenAIRE |
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