ON THE ISOPERIMETRIC DEFICIT UPPER LIMIT

Title & Authors
ON THE ISOPERIMETRIC DEFICIT UPPER LIMIT
Zhou, Jiazu; Ma, Lei; Xu, Wenxue;

Abstract
In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane $\small{\mathbb{R}^2}$ are investigated. The Minkowski mixed convex set of two convex sets K and L is studied and some new geometric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style inequalities for convex domain K are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema ([5]) and Pleijel ([22]).
Keywords
convex domain;the Minkowski mixed area;the isoperimetric deficit upper limit;the Bonnesen style inequality;the reverse Bonnesen style inequality;
Language
English
Cited by
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2.
On containment measure and the mixed isoperimetric inequality, Journal of Inequalities and Applications, 2013, 2013, 1, 540
3.
Reverse Bonnesen style inequalities in a surface $$\mathbb{X}_\varepsilon ^2$$ of constant curvature, Science China Mathematics, 2013, 56, 6, 1145
4.
Bonnesen-style symmetric mixed inequalities, Journal of Inequalities and Applications, 2016, 2016, 1
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