• Zhou, Jiazu ;
  • Ma, Lei ;
  • Xu, Wenxue
  • 투고 : 2011.07.10
  • 발행 : 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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피인용 문헌

  1. Bonnesen-style Wulff isoperimetric inequality vol.2017, pp.1, 2017,
  2. On containment measure and the mixed isoperimetric inequality vol.2013, pp.1, 2013,
  3. Reverse Bonnesen style inequalities in a surface $$\mathbb{X}_\varepsilon ^2$$ of constant curvature vol.56, pp.6, 2013,
  4. Bonnesen-style symmetric mixed inequalities vol.2016, pp.1, 2016,


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