Jørgensen不等式的推广
The Generalization of Jørgensen’s Inequality
摘要:
假设Möbius变换f和g生成一个离散群，我们得到下列Jørgensen不等式的推广：1：若
<f,g>为M的离散子群且γ≠β，则|γ+1|+|β+1|≥0.065…；2：若<f,g>为M的离散子群且β≠-3，则|γ+1|+|β+3|≥0.528…；3：若<f,g>为M的离散子群且β≠-4，则|γ+1|+|β+4|≥0.246…。
Abstract:
Assume that Möbius transformation f and g genenrate a discrete group. We obtain the following generalizations of Jørgensen’s inequalities: 1: If <f,g> is a subgroup of M and γ≠β, then |γ+1|+|β+1|≥0.065…; 2: If <f,g> is a subgroup of M and β≠-3, then |γ+1|+|β+3|≥0.528…; 3: If <f,g> is a subgroup of M and β≠-4, then |γ+1|+|β+4|≥0.246….
参考文献
|
[1]
|
Jørgensen, T. (1976) On Discrete Groups of Möbius Transformations. American Journal of Mathematics, 98, 737-749. [Google Scholar] [CrossRef]
|
|
[2]
|
Cao, C. (1995) Some Trace Inequalities for Discrete Groups of Möbius Transformations. Proceedings of the American Mathematical Society, 123, 3807-3815. [Google Scholar] [CrossRef]
|
|
[3]
|
Gehring, F.W. and Martin, G.J. (1991) Some Universal Constraints for Discrete Möbius Groups. Springer, New York. [Google Scholar] [CrossRef]
|
|
[4]
|
Tan, D. (1989) On Two-Generator Discrete Groups of Möbius Transformations. Proceedings of the American Mathematical Society, 106, 763-770. [Google Scholar] [CrossRef]
|
|
[5]
|
Gehring, F.W. and Martin, G.J. (1989) Stability and Extremality in Jørgensen’s Inequality. Complex Variables, Theory and Application, 12, 277-282. [Google Scholar] [CrossRef]
|