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http://dx.doi.org/10.4134/BKMS.2013.50.1.175

ON THE ISOPERIMETRIC DEFICIT UPPER LIMIT  

Zhou, Jiazu (School of Mathematics and Statistics Southwest University, Southeast Guizhou Vocational College of Technology for Nationalities)
Ma, Lei (Southeast Guizhou Vocational College of Technology for Nationalities)
Xu, Wenxue (School of Mathematics and Statistics Southwest University, Southeast Guizhou Vocational College of Technology for Nationalities)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.1, 2013 , pp. 175-184 More about this Journal
Abstract
In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane $\mathbb{R}^2$ 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;
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Times Cited By KSCI : 2  (Citation Analysis)
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