# ON THE ISOPERIMETRIC DEFICIT UPPER LIMIT

• Zhou, Jiazu ;
• Ma, Lei ;
• Xu, Wenxue
• 투고 : 2011.07.10
• 발행 : 2013.01.31
• 105 17

#### 초록

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]).

#### 키워드

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

#### 참고문헌

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#### 피인용 문헌

1. Bonnesen-style Wulff isoperimetric inequality vol.2017, pp.1, 2017, https://doi.org/10.1186/s13660-017-1305-3
2. On containment measure and the mixed isoperimetric inequality vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-540
3. Reverse Bonnesen style inequalities in a surface $$\mathbb{X}_\varepsilon ^2$$ of constant curvature vol.56, pp.6, 2013, https://doi.org/10.1007/s11425-013-4578-0
4. Bonnesen-style symmetric mixed inequalities vol.2016, pp.1, 2016, https://doi.org/10.1186/s13660-016-1146-5

#### 과제정보

연구 과제 주관 기관 : NSFC