JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (12): 94-102.doi: 10.6040/j.issn.1671-9352.0.2024.009

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On integral inequalities of mean curvature for convex bodies in Rn

LAN Yu, RAN Qiwei, ZENG Chunna*   

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
  • Published:2025-12-10

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Abstract: By applying integral inequalities for convex functions we obtain an estimate of the i-th order mean curvature integral powers of a convex body, thereby a strengthened form of Chen and Ros inequalities are given. Further more, by means of these obtained conclusions, we obtain the strengther form of Willmore inequality and Ross inequality, and an upper bound estimate for the curvature entropy inequality.

Key words: mean curvature integral inequality, Ros inequality, probability space, Willmore inequality

CLC Number: 

  • O186
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