On critical extremal length for the existence of holomorphic mappings of once-holed tori

被引：2
|
作者：
Masumoto, Makoto [1 ]
机构：
[1] Yamaguchi Univ, Dept Math, Yamaguchi 7538512, Japan
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2013年
关键词：
Riemann surface; once-holed torus; holomorphic mapping; extremal length;
D O I：
10.1186/1029-242X-2013-282
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let be the set of marked once-holed tori which allows a holomorphic mapping into a given Riemann surface with marked handle. We compare it with the subset of marked once-holed tori X such that there is a holomorphic mapping for which the cardinal numbers of , , are bounded. We show that while is a proper subset of apart from a few exceptions, their critical extremal lengths are identical. MSC: 30F99, 32H02.
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