On Bonnesen-style symmetric mixed inequality of two planar convex domains
On Bonnesen-style symmetric mixed inequality of two planar convex domains
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DOI：
10.1360/012014-58
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
Pengfu Wang;Wenxue Xu;Jiazu Zhou;Baocheng Zhu
中科院分区：
文献类型：
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作者：
Pengfu Wang;Wenxue Xu;Jiazu Zhou;Baocheng Zhu
利用积分几何中已知的Poincare和Blaschke运动学公式，研究了欧氏平面R2中区域K0和K1的对称混合等周亏损Δ2（K0，K1）.得到了对称混合等周不等式和Bonnesen型对称混合不等式。其中一个不等式强化了Kotlyars不等式。最后，我们得到了一些逆Bonnesen型对称混合不等式，推广了已知的Bottemas结果.
investigate the symmetric mixed isoperimetric deficit Δ2( K 0, K 1) of domains K 0 and K 1 in the Euclidean plane R 2 via the known kinematic formulas of Poincare and Blaschke in integral geometry. Then we obtain symmetric mixed isoperimetric inequality and some Bonnesen-style symmetric mixed inequalities. One of those inequalities strengthens Kotlyars inequality. Finally, we obtain some reverse Bonnesen-style symmetric mixed inequalities that generalize the known Bottemas result.