• Zhou, Jiazu ;
  • Ma, Lei ;
  • Xu, Wenxue
  • Received : 2011.07.10
  • Published : 2013.01.31


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]).


convex domain;the Minkowski mixed area;the isoperimetric deficit upper limit;the Bonnesen style inequality;the reverse Bonnesen style inequality


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