NOTES ON THE LOG-MINKOWSKI INEQUALITY OF CURVATURE ENTROPY

NOTES ON THE LOG-MINKOWSKI INEQUALITY OF CURVATURE ENTROPY

NOTES ON THE LOG-MINKOWSKI INEQUALITY OF CURVATURE ENTROPY

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doi:10.1007/s10473-025-0102-1

Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (1): 16-26.doi: 10.1007/s10473-025-0102-1

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Deyi LI¹, Lei MA², Chunna ZENG^3,*

1. School of Science, Wuhan University of Science and Technology, Wuhan 430081, China;
2. School of Sciences, Guangdong Preschool Normal College in Maoming, Maoming 525200, China;
3. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received:2024-07-04 Revised:2024-10-23 Published:2025-02-06
Contact: *Chunna ZENG, E-mail,: engchn@163.com
About author:Deyi LI, E-mail,: lideyi@wust.edu.cn; Lei MA, E-mail,: maleiyou@163.com
Supported by:
Li's work was supported by the NSFC (12171378); Ma's work was supported by the Characteristic innovation projects of universities in Guangdong province (2023KTSCX381); Zeng's work was supported by the Young Top-Talent program of Chongqing (CQYC2021059145), the Major Special Project of NSFC (12141101), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZD-K202200509) and the Natural Science Foundation Project of Chongqing (CSTB2024NSCQ-MSX0937).

Abstract: An upper estimate of the new curvature entropy is provided, via the integral inequality of a concave function. For two origin-symmetric convex bodies in $\mathbb{R}^n$ , this bound is sharper than the log-Minkowski inequality of curvature entropy. As its application, a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.

Key words: convex bodies, the log-Minkowski inequality, curvature entropy, the log-Minkowski inequality of curvature entropy

CLC Number:

52A22

Deyi LI, Lei MA, Chunna ZENG. NOTES ON THE LOG-MINKOWSKI INEQUALITY OF CURVATURE ENTROPY[J].Acta mathematica scientia,Series B, 2025, 45(1): 16-26.

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