Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 641-650.

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The General Inverse Bonnesen-Style Inequalities in $\mathbb{R}^n$

Xu Dong1(),Yan Zhang1(),Chunna Zeng1,*(),Xingxing Wang2()   

  1. 1 School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
    2 School of Mathematics and Statistics, Shanghai Lixin University of Accounting and Finance, Shanghai 201620
  • Received:2021-08-04 Online:2022-06-26 Published:2022-05-09
  • Contact: Chunna Zeng;;;
  • Supported by:
    the NSFC(11801048);the Young Top-Talent Program of Chongqing(CQYC2021059145);the NSF of Chongqing(cstc2020jcyj-msxmX0609);the Venture Innovation Support Program for Chongqing Overseas Returnees(cx2018034);the Venture Innovation Support Program for Chongqing Overseas Returnees(cx2019155);the Technology Research Foundation of Chongqing Educational Committee(KJQN201900530)


The isoperimetric problem plays an important role in integral geometry. In this paper we mainly investigate the inverse form of the isoperimetric inequality, i.e. the general inverse Bonnesen-type inequalities. The upper bounds of several new general isoperimetric genus are obtained. Futhermore, as corollaries, we get a series of classical inverse Bonnesen-type inequalities in the plane. Finally, the best estimate between the results of three upper bounds is given.

Key words: Aleksandrov-fenchel inequalities, Inverse Bonnesen type inequality, Quermassintegrals

CLC Number: 

  • O186.5