| Finite Degree Holomorphic Covers of Compact Riemann Surfaces |
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| 引用本文： | Jouni PARKKONEN Vesa RUUSKA. Finite Degree Holomorphic Covers of Compact Riemann Surfaces[J]. 数学学报(英文版), 2007, 23(1): 89-94. DOI: 10.1007/s10114-005-0824-x |
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| 作者姓名： | Jouni PARKKONEN Vesa RUUSKA |
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| 作者单位： | [1]Department of Mathematics and Statistics, P,O. Box 35, 40014 University of Jyvaeskylae, Finland [2]Department of Physics, P.O. Box 35, 40014 University of Jyvaeskylae Finland |
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| 基金项目： | The first author is supported by the Center of Excellence ＂Geometric Analysis and Mathematical Physics＂ of the Academy of Finland |
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| 摘 要： |
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| 关 键 词： | 黎曼表面 遮盖图 准共形图 数学分析 |
| 收稿时间： | 2004-03-18 |
| 修稿时间： | 2004-03-182005-03-01 |
Finite Degree Holomorphic Covers of Compact Riemann Surfaces |
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| Jouni Parkkonen,Vesa Ruuska. Finite Degree Holomorphic Covers of Compact Riemann Surfaces[J]. Acta Mathematica Sinica(English Series), 2007, 23(1): 89-94. DOI: 10.1007/s10114-005-0824-x |
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| Authors: | Jouni Parkkonen Vesa Ruuska |
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| Affiliation: | 1. Department of Mathematics and Statistics, University of Jyv?skyl?, 35, 40014, Finland
2. Department of Physics, University of Jyv?skyl?, 35, 40014, Finland
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| Abstract: | A conjecture of Ehrenpreis states that any two compact Riemann surfaces of genus at least two have finite degree unbranched holomorphic covers that are arbitrarily close to each other in moduli space. Here we prove a weaker result where certain branched covers associated with arithmetic Riemann surfaces are allowed, and investigate the connection of our result with the original conjecture. |
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| Keywords: | Riemann surfaces covering maps quasiconformal maps |
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