Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1249-1262.

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Bonnesen-Style Inequalities for Star Bodies

Zengle Zhang()   

  1. Chongqing Key Laboratory of Group & Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing 402160
  • Received:2020-10-22 Online:2021-10-26 Published:2021-10-08
  • Supported by:
    the NSF of Chongqing(cstc2020jcyj-msxmX0779);the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN201901312)


Motivated by works of Lutwak and Petty[25-26, 37], a new star body ${\cal G}K$ associated with a given convex body $K$ is constructed. The isoperimetric inequality for ${\cal G}K$ and the reverse Bonnesen-style inequalities for K are established.

Key words: isoperimetric inequality, Bonnesen-style isoperimetric Inequality, Differential affine isoperimetric inequality, Star body

CLC Number: 

  • O186.5