Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 3-15

ASYMPTOTIC BEHAVIOUR OF THE RIEMANN MAPPING FUNCTION AT ANALYTIC CUSPS

Tobias Kaiser and Sabrina Lehner

University of Passau, Faculty of Computer Science and Mathematics
D-94030 Passau, Germany; tobias.kaiser 'at' uni-passau.de

University of Passau, Faculty of Computer Science and Mathematics
D-94030 Passau, Germany; sabrina.lehner 'at' uni-passau.de

Abstract. We completely describe the asymptotic behaviour of the Riemann mapping function and its derivatives at an analytic cusp. We achieve the same for the inverse of the mapping function.

2010 Mathematics Subject Classification: Primary 30C20, 30E15.

Key words: Mapping function, analytic cusp, asymptotic behaviour.

Reference to this article: T. Kaiser and S. Lehner: Asymptotic behaviour of the Riemann mapping function at analytic cusps. Ann. Acad. Sci. Fenn. Math. 42 (2017), 3-15.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4201