Bounded Projective Functions and Hyperbolic Metrics with Isolated Singularities
Differential Geometry
2019-01-11 v2 Analysis of PDEs
Complex Variables
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 . As an application, we construct explicitly a new class of hyperbolic metrics with countably many singularities on the unit disc.
Cite
@article{arxiv.1709.03112,
title = {Bounded Projective Functions and Hyperbolic Metrics with Isolated Singularities},
author = {Bo Li and Yu Feng and Long Li and Bin Xu},
journal= {arXiv preprint arXiv:1709.03112},
year = {2019}
}
Comments
14 pages. We revised the old version greatly. In particular, we changed the title a little bit, generalized the main theorem to general Riemann surface, added a complex analytical definition for cone/cusp singularity of hyperbolic metric and Example 1.1