Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 875-887

ESTIMATES OF THE HYPERBOLIC METRIC ON THE TWICE PUNCTURED PLANE

Seong-A Kim, Jinxi Ma and William Ma

Dongguk University, Department of Mathematics Education
Gyeongju, 780-714, Korea; sakim 'at' dongguk.ac.kr

Beihang University, Department of Mathematics
Haidian District, Beijing 100083, P.R. China; majinxi 'at' buaa.edu.cn

Pennsylvania College of Technology, School of Sciences, Humanities & Visual Communications
Williamsport, PA 17701, U.S.A.; wma 'at' pct.edu

Abstract. We provide various estimates of the hyperbolic metric on the twice punctured plane C \ {0,1} and apply them to improve Landau's Theorem. We also improve Ahlfors' upper bound for the hyperbolic metric on the twice punctured plane C \ {0,1}.

2010 Mathematics Subject Classification: Primary 30C80; Secondary 30F45, 53A35.

Key words: Hyperbolic metric, Landau's Theorem.

Reference to this article: S. Kim, J. Ma and W. Ma: Estimates of the hyperbolic metric on the twice punctured plane. Ann. Acad. Sci. Fenn. Math. 40 (2015), 875-887.

Full document as PDF file

doi:10.5186/aasfm.2015.4058