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1. DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC ${D}^n | |||
wangjianfei ,Liu Taishun,Tang Xiaomin | |||
Mathematics 13 January 2009 | |||
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Abstract:In this paper, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc $D^n$ with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds on $|\\\\det (f\\\ | |||
TO cite this article: wangjianfei ,Liu Taishun,Tang Xiaomin. DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC ${D}^n[OL].[13 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27735 |
2. Distortion theorems on the Lie ball RIV(n) in Cn | |||
wangjianfei,Liu Taishun,Xu Huiming | |||
Mathematics 12 January 2009 | |||
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Abstract:In this paper, we introduce the subfamilies Hm(RIV(n)) of holomorphic mappings defined on the Lie ball RIV(n) which take into consideration the m-order to which the Jacobian determinant must vanish, as well as for the limiting case of locally biholomorphic mappings. Various distortion theorems for holomophic mappings Hm(RIV(n)) are established. The distortion theorems coincide with Liu and Minda as the special case of the unit disk. When m = 1 and m ! +1, the distortion theoerems reduce to the results obtained by Gong for RIV(n), respectively. Moreover, our method is different. As an application, the bounds for Bloch constants of Hm(RIV(n)) are given. | |||
TO cite this article:wangjianfei,Liu Taishun,Xu Huiming. Distortion theorems on the Lie ball RIV(n) in Cn[OL].[12 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27691 |
3. On the solution of Dirichlet’s problem of complex Monge-Amp`ere equation on Cartan-Hartogs domain of the second type | |||
Yin Weiping,Yin Xiaolan | |||
Mathematics 26 May 2008 | |||
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Abstract:Complex Monge-Amp`ere equation is a nonlinear equation with high degree, therefore to get its solution is very difficult. In present paper how to get the solution of Dirichlet’s problem of Complex Monge-Amp`ere equation on the Cartan-Hartogs domain of the second type is discussed by using the analytic method. Firstly, the complex Monge-Amp`ere equation is reduced to the nonlinear ordinary differential equation, then the solution of the Dirichlet’s problem of complex Monge-Amp`ere equation is reduced to the solution of two point boundary value problem of the nonlinear second-order ordinary differential equation. Secondly, the solution of the Dirichlet’s problem is given in semiexplicit formula, and under the special case the exact solution is obtained. These results may be helpful for the numerical method of Dirichlet’s problem of complex Monge-Amp`ere equation on the Cartan-Hartogs domain. | |||
TO cite this article:Yin Weiping,Yin Xiaolan. On the solution of Dirichlet’s problem of complex Monge-Amp`ere equation on Cartan-Hartogs domain of the second type[OL].[26 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21774 |
4. On the solution of Dirichlet’s problem of complex Monge-Amp`ere equation on Cartan-Hartogs domain of the first type | |||
Yin Weiping,Yin Xiaolan | |||
Mathematics 15 May 2008 | |||
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Abstract:Complex Monge-Amp`ere equation is a nonlinear equation with high degree, therefore to get its solution is very difficult. In present paper how to get the solution of Dirichlet’s problem of Complex Monge-Amp`ere equation on the Cartan-Hartogs domain of the first type is discussed by using the analytic method. Firstly, the complex Monge-Amp`ere equation is reduced to the nonlinear ordinary differential equation, then the solution of the Dirichlet’s problem of complex Monge-Amp`ere equation is reduced to the solution of two point boundary value problem of the nonlinear second-order ordinary differential equation. Secondly, the solution of the Dirichlet’s problem is given in semiexplicit formula, and under the special case the exact solution is obtained. These results may be helpful for the numerical method of Dirichlet’s problem of complex Monge-Amp`ere equation on the Cartan-Hartogs domain. | |||
TO cite this article:Yin Weiping,Yin Xiaolan. On the solution of Dirichlet’s problem of complex Monge-Amp`ere equation on Cartan-Hartogs domain of the first type[OL].[15 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21446 |
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