交比在k-拟共形映射下的偏差

• 机 构: 安徽财经大学统计与应用数学学院
• 出 处: 黑龙江大学(自然科学学报)
• 发表日期: 2012年4期
• 关键词: η-distortion function of Agard k-qusasiconformal mappings cross ratio distortion

研究Agard的η-偏差函数与k-拟共形映射上(下)界的关系,应用Agard的η-偏差函数的性质,给出k-拟共形映射上(下)界的表达式;得到交比在k-拟共形映射下的偏差估计:若f(z)∈Q,则[exp(1/k-k)π]︱(z1,z2,z3,z4)︱km≤︱(f(z1),f(z2)f(z3),f(z4))︱≤[exp(k-1/k)π]︱(z1,z2,z3,z4)︱kn其中,当︱(z1,z2,z3,z4)︱≤1,时n=-1,m=1;当︱(z1,z2,z3,z4)︱>1时,n=1,m=-1.且︱(z1,z2,z3,z4)︱=(z1-z3)(z2-z4)/(z1-z4)(z2-z3)表示扩充复平面C珔2上不同四点的交比.“,”The relation of upper(lower) bound of k-qusasiconformal mappings and η-distortion function of Agard was studied.By means of the properties of η-distortion function of Agard,the expressions of upper(lower) bound of k-qusasiconformal mappings were given.And the distortion estimator of cross ratio under k-qusasiconformal mappings was obtained,that is,if f(z)∈Q,then [exp(1/k-k)π]︱(z1,z2,z3,z4)︱km≤︱(f(z1),f(z2)f(z3),f(z4))︱≤[exp(k-1/k)π]︱(z1,z2,z3,z4)︱kn where︱(z1,z2,z3,z4)︱=(z1-z3)(z2-z4)/(z1-z4)(z2-z3),n=-1 and m=1 for︱(z1,z2,z3,z4)︱≤1,n=1 and m=-1 for︱(z1,z2,z3,z4)︱>1.