Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 687–698

BOUNDED PROJECTIVE FUNCTIONS AND HYPERBOLIC METRICS WITH ISOLATED SINGULARITIES

Bo Li, Long Li and Bin Xu

Chinese Academy of Science, USTC, Wu Wen-Tsun Key Laboratory of Mathematics
and University of Science and Technology of China, School of Mathematical Sciences
No. 96 Jinzhai Road, Hefei, Anhui Province 230026, P.R. China; ilozyb 'at' mail.ustc.edu.cn

University of Iceland, Science Institute
Dunhaga 5, 107 Reykjavík, Iceland; longli 'at' hi.is

Abstract. We establish a correspondence on a Riemann surface between hyperbolic metrics with isolated singularities and bounded projective functions whose Schwarzian derivatives have at most double poles and whose monodromies lie in PSU(1,1). As an application, we construct explicitly a new class of hyperbolic metrics with countably many singularities on the unit disc.

2010 Mathematics Subject Classification: Primary 51M10; Secondary 35J61, 34M35.

Key words: Hyperbolic metric with singularities, projective function.

Reference to this article: B. Li, L. Li and B. Xu: Bounded projective functions and hyperbolic metrics with isolated singularities. Ann. Acad. Sci. Fenn. Math. 45 (2020), 687–698.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4539