Constructing Strebel differentials via Belyi maps on the Riemann sphere
Constructing Strebel differentials via Belyi maps on the Riemann sphere
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DOI：
10.1007/s40315-020-00302-3
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发表时间：
2020
影响因子：
2.1
通讯作者：
许斌
中科院分区：
文献类型：
--
作者：
宋基建;许斌
In this paper, by using Belyi maps and dessin d’enfants, we construct some concrete examples of Strebel differentials with four double poles of residues 1, 1, 1, 1 on the Riemann sphere. We also prove that they have either two double zeroes or four simple zeroes. In particular, we show that they have two double zeroes if and only if their poles are coaxial; in such cases we also obtain their explicit expressions. On the other hand, for those differentials with four non-coaxial poles and whose metric ribbon graphs have edges of rational lengths, we characterize them optimally in terms of Belyi maps in the sense that the Belyi maps used here have minimal degree, and work out the explicit expressions of the five simplest ones among them. As applications, we obtain some explicit cone spherical metrics on the Riemann sphere...This is a preview of subscription content, log in to check access...
