Compact non-orientable surfaces of genus 6 with extremal metric discs
Compact non-orientable surfaces of genus 6 with extremal metric discs
复制标题
具有极值公制圆盘的 6 类紧凑不可定向表面
DOI：
10.1090/ecgd/298
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发表时间：
2016
影响因子：
0.6
通讯作者：
Gou Nakamura
中科院分区：
文献类型：
--
作者：
Makoto Abe;Gou Nakamura;Makoto Masumoto;Gou Nakamura
一个亏格的紧致双曲曲面称为极值曲面，如果它有一个极值圆盘，这个圆盘的最大半径仅由。讨论亏格为6的不可定向极值曲面中嵌入了多少个极值圆。这是我们感兴趣的最后一个属，因为它已经被称为，或。我们证明亏格6的不可定向极曲面最多允许两个极圆。极值盘的轨迹也得到了每个表面。因此，任意亏格的不可定向的极值曲面至多允许两个极值圆。此外，我们确定了亏格为6的具有两个极值圆的不可定向极值曲面的自同构群。引用
A compact hyperbolic surface of genusis said to be extremal if it admits an extremal disc, a disc of the largest radius determined only by. We discuss how many extremal discs are embedded in non-orientable extremal surfaces of genus 6. This is the final genus in our interest because it is already known for, or. We show that non-orientable extremal surfaces of genus 6 admit at most two extremal discs. The locus of extremal discs is also obtained for each surface. Consequently non-orientable extremal surfaces of arbitrary genusadmit at most two extremal discs. Furthermore we determine the groups of automorphisms of non-orientable extremal surfaces of genus 6 with two extremal discs. References