NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY*

doi:10.1007/s10473-023-0601-x

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2333-2346.doi: 10.1007/s10473-023-0601-x

• • 下一篇

NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY^*

Yunlong YANG¹, Nan JIANG¹, Deyan ZHANG^2,†

1. School of Science, Dalian Maritime University, Dalian 116026, China;
2. School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, China

收稿日期:2022-05-27 修回日期:2023-05-19 发布日期:2023-12-08
通讯作者: †Deyan ZHANG, E-mail: zhangdy8005@126.com
作者简介:Yunlong YANG, E-mail: ylyang@dlmu.edu.cn; Nan JIANG, E-mail: 995125315@qq.com
基金资助:
Supported by the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (gxyqZD2020022), the University Natural Science Research Project of Anhui Province (2022AH040067), the Fundamental Research Funds for the Central Universities (3132023202) and National Natural Science Foundation of China (12001080).

NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY^*

Yunlong YANG¹, Nan JIANG¹, Deyan ZHANG^2,†

1. School of Science, Dalian Maritime University, Dalian 116026, China;
2. School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, China

Received:2022-05-27 Revised:2023-05-19 Published:2023-12-08
Contact: †Deyan ZHANG, E-mail: zhangdy8005@126.com
About author:Yunlong YANG , E-mail: ylyang@dlmu.edu.cn; Nan JIANG, E-mail: 995125315@qq.com
Supported by:
Supported by the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (gxyqZD2020022), the University Natural Science Research Project of Anhui Province (2022AH040067), the Fundamental Research Funds for the Central Universities (3132023202) and National Natural Science Foundation of China (12001080).

摘要/Abstract

摘要： Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality. In this paper, we investigate the relative positive center set of planar convex bodies. As an application of the relative positive center, we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.

关键词: cone-volume measure, dilation position, log-Brunn-Minkowski's inequality, log-Minkowski's inequality, relative positive center

Abstract: Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality. In this paper, we investigate the relative positive center set of planar convex bodies. As an application of the relative positive center, we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.

Key words: cone-volume measure, dilation position, log-Brunn-Minkowski's inequality, log-Minkowski's inequality, relative positive center

中图分类号:

52A40

Yunlong YANG, Nan JIANG, Deyan ZHANG. NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY^*[J]. 数学物理学报(英文版), 2023, 43(6): 2333-2346.

Yunlong YANG, Nan JIANG, Deyan ZHANG. NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2333-2346.

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NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY^*

NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY^*

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