| 两平面凸域的对称混合等周不等式 |
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| 引用本文： | 曾春娜,周家足,岳双珊.两平面凸域的对称混合等周不等式[J].数学学报,2012(2):355-362. |
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| 作者姓名： | 曾春娜 周家足 岳双珊 |
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| 作者单位： | 西南大学数学与统计学院;黔东南民族职业技术学院 |
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| 基金项目： | 国家自然科学基金资助项目(10971167) |
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| 摘 要： | 设K_k(k=i,j)为欧氏平面R~2中面积为A_k,周长为P_k的域,它们的对称混合等周亏格(symmetric mixed isoperimetric deficit)为σ(K_i,K_j)=P_i~2P_j~2-16π~2A_iA_j.根据周家足,任德麟(2010)和Zhou,Yue(2009)中的思想,用积分几何方法,得到了两平面凸域的Bonnesen型对称混合不等式及对称混合等周不等式,给出了两域的对称混合等周亏格的一个上界估计.还得到了两平面凸域的离散Bonnesen型对称混合不等式及两凸域的对称混合等周亏格的一个上界估计,并应用这些对称混合(等周)不等式估计第二类完全椭圆积分.
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| 关 键 词： | 对称混合等周亏格 对称混合等周不等式 Bonnesen型对称混合不等式 |
The Symmetric Mixed Isoperimetric Inequality of Two Planar Convex Domains |
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| Chun Na ZENG School of Mathematics and Statistics,Southwest University,Chongqing,P.R.China Jia Zu ZHOU School of Mathematics and Statistics,Southwest University,Chongqing,P.R.China Southeast Guizhou Vocational College of Technology for Nationalities, Kaili,P.R.China Shuang Shan YUE.The Symmetric Mixed Isoperimetric Inequality of Two Planar Convex Domains[J].Acta Mathematica Sinica,2012(2):355-362. |
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| Authors: | Chun Na ZENG School of Mathematics and Statistics Southwest University Chongqing PRChina Jia Zu ZHOU School of Mathematics and Statistics Southwest University Chongqing PRChina Southeast Guizhou Vocational College of Technology for Nationalities Kaili PRChina Shuang Shan YUE |
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| Affiliation: | School of Mathematics and Statistics,Southwest University,Chongqing 400715,P.R.China |
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| Abstract: | Let K_k(k =i,j) be domain of the area A_k,and of the perimeter P_k, respectively.The symmetric mixed isoperimetric deficit of K_i and K_j is defined asσ(K_i,K_j) = P_i~2P_j~2-16π~2A_iA_j.We follow the ideas of Zhou,Ren(2010) and Zhou, Yue(2009) and obtain some Bonnesen-style symmetric mixed inequalities and the symmetric mixed isoperimetric inequality by the method of integral geometry.We also obtain some symmetric mixed isoperimetric upper limits.Some discrete Bonnesen-style symmetric mixed inequalities and one upper limit of the discrete symmetric mixed isoperimetric deficit for two domains are obtained.Finally we apply these symmetric mixed(isoperimetric) inequalities to estimate the complete elliptic integral of second class. |
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| Keywords: | The symmetric mixed isoperimetric deficit the symmetric mixed isoperimetric inequality the Bonnesen-style symmetric mixed inequality |
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