有关Clifford矩阵群的几个离散性判别准则
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摘要
研究了Clifford矩阵变换群的离散性质,给出了几个判别离散群的不等式和定理.
In this paper, the discreteness of Clifford matrix groups is studied and several discreteness criteria and inequalities are obtained.
In this paper, the discreteness of Clifford matrix groups is studied and several discreteness criteria and inequalities are obtained.
引文
[1] Beardon A F. The geometry of discrete groups[M]. Berlin, New York:Springer-Verlag,1983.
[2] Fang A N, Nai B. On the discreteness and convergence in n-dimensional Mobius groups[J]. J London Math Soc, 2000, 61:761-773.
[3] Fang A N, Nai B. On algebraic convergence of Clifford matrix groups[J]. Chin Ann Math Ser A, 2000, 21(1):369-376.
[4] Maskit B. Kleinian groups[M]. Berlin, New York:Springer-Verlag, 1987.
[5] Waterman P L. Mbius transformations in several dimensions[J].Adv in Math, 1993,101:87-113.
[6] J?rgensen T. On discrete groups of Mobius transformations[J]. Amer J Math, 1976,98:739-749.
[7] J?rgensen T. Comments on a discreteness condition for subgroups of SL(2,C)[J].Canad J Math, 1979, 31:87-92.
[8] Abikoff W, Hass A. Non-discrete groups of hyperbolis motions[J]. Bull London Math Soc, 1990, 22:233-238.
[9] Martin G J. On the discrete Mobius groups in all dimensions[J]. Acta Math, 1989,163:253-289.
[10] Martin G J. On discrete isometry groups of negative curvature[J]. Pacific J Math,1993, 160:109-127.
[11] Gehring F W,Martin G J. Discrete guasiconformal groups[J]. Proc London Math Soc,1987, 55:331-358.
[12] Wang X T,Yang W Q. Discreteness criteria of M(o|¨)bius groups of high dimensions and convergence theorem of kleinian groups[J]. Adv in Math, 2001, 159:68-82.
[13] Wang X T. Dense subgroups of n-dimensional Mobius groups[J]. Math Zeit, 1999,38:29-34.
[14] Jiang Y P. On the discreteness of Mobius groups in all dimensions[J]. Math Proc Camb Phi Soc, 2004, 138:547-555.
[15] Jiang Y P, Kamiya S, Parker J R. J?rgensen's inequalitiy for complex hyperbolic space[J]. Geom Dedicata, 2003, 97:55-80.
[16] Chen M. Discreteness and convergence of Mobius groups[J]. Geom Dedicata, 2004,104:61-69.
[17] Li L, Fu X. Discreteness by use a test map[J]. Bull Korean Math Soc, 2012, 49(1):57-61.
[18] Dai B L. Discreteness criteria for subgroups of isometry groups of pinched Hadamard manifolds by use of a test map[J]. Acta Mathematica Sinica, 2013, 56A(6):935-940.
[19] Tan D. On two-generator discrete groups of Mobius transformations[J]. Proc Amer Math Soc, 1989, 106(3):63-770.
[20] Wang J, Dai B L. Inequalities and common fixed points for M(o|¨)bius groups in R~n[J].Scientiae Mathematicae, 1999, 3(2):385-392.
[21] Zhu R R. Inequalities about discretiness of transformation groups[D]. Shanghai,Shanghai University of Finance and Economics, 2016.
[22] Yang S, Zhao T. Conjugacy class and discreteness in SL(2, C)[J]. Osaka J Math, 2016,53:1047-1053.
[2] Fang A N, Nai B. On the discreteness and convergence in n-dimensional Mobius groups[J]. J London Math Soc, 2000, 61:761-773.
[3] Fang A N, Nai B. On algebraic convergence of Clifford matrix groups[J]. Chin Ann Math Ser A, 2000, 21(1):369-376.
[4] Maskit B. Kleinian groups[M]. Berlin, New York:Springer-Verlag, 1987.
[5] Waterman P L. Mbius transformations in several dimensions[J].Adv in Math, 1993,101:87-113.
[6] J?rgensen T. On discrete groups of Mobius transformations[J]. Amer J Math, 1976,98:739-749.
[7] J?rgensen T. Comments on a discreteness condition for subgroups of SL(2,C)[J].Canad J Math, 1979, 31:87-92.
[8] Abikoff W, Hass A. Non-discrete groups of hyperbolis motions[J]. Bull London Math Soc, 1990, 22:233-238.
[9] Martin G J. On the discrete Mobius groups in all dimensions[J]. Acta Math, 1989,163:253-289.
[10] Martin G J. On discrete isometry groups of negative curvature[J]. Pacific J Math,1993, 160:109-127.
[11] Gehring F W,Martin G J. Discrete guasiconformal groups[J]. Proc London Math Soc,1987, 55:331-358.
[12] Wang X T,Yang W Q. Discreteness criteria of M(o|¨)bius groups of high dimensions and convergence theorem of kleinian groups[J]. Adv in Math, 2001, 159:68-82.
[13] Wang X T. Dense subgroups of n-dimensional Mobius groups[J]. Math Zeit, 1999,38:29-34.
[14] Jiang Y P. On the discreteness of Mobius groups in all dimensions[J]. Math Proc Camb Phi Soc, 2004, 138:547-555.
[15] Jiang Y P, Kamiya S, Parker J R. J?rgensen's inequalitiy for complex hyperbolic space[J]. Geom Dedicata, 2003, 97:55-80.
[16] Chen M. Discreteness and convergence of Mobius groups[J]. Geom Dedicata, 2004,104:61-69.
[17] Li L, Fu X. Discreteness by use a test map[J]. Bull Korean Math Soc, 2012, 49(1):57-61.
[18] Dai B L. Discreteness criteria for subgroups of isometry groups of pinched Hadamard manifolds by use of a test map[J]. Acta Mathematica Sinica, 2013, 56A(6):935-940.
[19] Tan D. On two-generator discrete groups of Mobius transformations[J]. Proc Amer Math Soc, 1989, 106(3):63-770.
[20] Wang J, Dai B L. Inequalities and common fixed points for M(o|¨)bius groups in R~n[J].Scientiae Mathematicae, 1999, 3(2):385-392.
[21] Zhu R R. Inequalities about discretiness of transformation groups[D]. Shanghai,Shanghai University of Finance and Economics, 2016.
[22] Yang S, Zhao T. Conjugacy class and discreteness in SL(2, C)[J]. Osaka J Math, 2016,53:1047-1053.