Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (4): 985-993.

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Some Reverse Bonnesen-style Inequalities in $n$-Dimensional Euclidean Space $\mathbb{R} ^n$

Wang Hejun()   

  1. School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250358
  • Received:2022-01-14 Revised:2023-02-06 Online:2023-08-26 Published:2023-07-03
  • Contact: Hejun Wang E-mail:wanghjmath@sdnu.edu.cn
  • Supported by:
    China Postdoctoral Science Foundation(2020M682222);Natural Science Foundation of Shandong Province(ZR2020QA003);Natural Science Foundation of Shandong Province(ZR2020QA004)

Abstract:

This paper mainly studies reverse Bonnesen-style inequalities in $n$-dimensional Euclidean space $\mathbb{R} ^n$. By the Urysohn inequality, the dual isoperimetric inequality, mean width and mean intersection area, some new reverse Bonnesen-style inequalities for general convex bodies are obtained in $\mathbb{R} ^n$.

Key words: Reverse Bonnesen-style inequality, Isoperimetric deficit, Mean width, Mean intersection area

CLC Number: 

  • O186.5
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