### Abstract

Original language | English |
---|---|

Title of host publication | Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry |

Editors | Francis Bonahon, Robert L Devaney, Frederick P Gardiner, Dragomir Saric |

Place of Publication | Rhode Island USA |

Publisher | American Mathematical Society |

Pages | 147 - 157 |

Number of pages | 11 |

Volume | 573 |

ISBN (Print) | 9780821853481 |

DOIs | |

Publication status | Published - 2012 |

Event | Conference on Conformal Dynamics and Hyperbolic Geometry 2010 - Graduate School and University Center of CUNY, New York, United States of America Duration: 21 Oct 2010 → 23 Oct 2010 |

### Conference

Conference | Conference on Conformal Dynamics and Hyperbolic Geometry 2010 |
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Country | United States of America |

City | New York |

Period | 21/10/10 → 23/10/10 |

### Cite this

*Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry*(Vol. 573, pp. 147 - 157). Rhode Island USA: American Mathematical Society. https://doi.org/10.1090/conm/573/11377

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*Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry.*vol. 573, American Mathematical Society, Rhode Island USA, pp. 147 - 157, Conference on Conformal Dynamics and Hyperbolic Geometry 2010, New York, United States of America, 21/10/10. https://doi.org/10.1090/conm/573/11377

**The rate of convergence of the hyperbolic density on sequences of domains.** / Lakic, Nikola; Markowsky, Gregory Tycho.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - The rate of convergence of the hyperbolic density on sequences of domains

AU - Lakic, Nikola

AU - Markowsky, Gregory Tycho

PY - 2012

Y1 - 2012

N2 - It is known that if a sequence of domains U-n converges to a domain U in the Caratheodory sense then the hyperbolic densities on U-n converge to the hyperbolic density on U. In this paper, we study the rate of convergence of the hyperbolic density under a slightly different mode of convergence. In doing so, we are led to consider two other densities on domains, the Teichmuller density and the three-point density. We obtain several results which give rates of convergence in various scenarios.

AB - It is known that if a sequence of domains U-n converges to a domain U in the Caratheodory sense then the hyperbolic densities on U-n converge to the hyperbolic density on U. In this paper, we study the rate of convergence of the hyperbolic density under a slightly different mode of convergence. In doing so, we are led to consider two other densities on domains, the Teichmuller density and the three-point density. We obtain several results which give rates of convergence in various scenarios.

UR - http://arxiv.org/abs/1210.1619

U2 - 10.1090/conm/573/11377

DO - 10.1090/conm/573/11377

M3 - Conference Paper

SN - 9780821853481

VL - 573

SP - 147

EP - 157

BT - Contemporary Mathematics - Conformal Dynamics and Hyperbolic Geometry

A2 - Bonahon, Francis

A2 - Devaney, Robert L

A2 - Gardiner, Frederick P

A2 - Saric, Dragomir

PB - American Mathematical Society

CY - Rhode Island USA

ER -