Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2011.07.10
  • Published : 2013.01.31
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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]).

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References

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