Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 37, 2012, 191-201
University of Würzburg, Department of Mathematics
97074 Würzburg, Germany; sebastian.schleissinger 'at' mathematik.uni-wuerzburg.de
Abstract. We consider the chordal Loewner differential equation for multiple slits in the upper half-plane and relations between the pointwise Hölder continuity of the driving functions and the generated hulls. The first result generalizes a result of Lind that gives a sufficient condition for driving functions to generate simple curves. The second result translates the property that the hulls locally look like straight lines at their starting points into a condition for the driving functions.
2010 Mathematics Subject Classification: Primary 30C20, 30C35.
Key words: Univalent function, Loewner equation, slit map, slit domain.
Reference to this article: S. Schleissinger: The multiple-slit version of Loewner's differential equation and pointwise Hölder continuity of driving functions. Ann. Acad. Sci. Fenn. Math. 37 (2012), 191-201.
doi:10.5186/aasfm.2012.3720
Copyright © 2012 by Academia Scientiarum Fennica