## The log-Brunn-Minkowski inequality in $\mathbb {R}^3$

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- by Yunlong Yang and Deyan Zhang PDF
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**147**(2019), 4465-4475 Request permission

## Abstract:

Böröczky, Lutwak, Yang, and Zhang have recently proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane which is stronger than the classical Brunn-Minkowski inequality. This paper establishes the log-Brunn-Minkowski, log-Minkowski, $L_p$-Minkowski, and $L_p$-Brunn-Minkowski inequalities for two classes of convex bodies in $\mathbb {R}^3$.## References

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## Additional Information

**Yunlong Yang**- Affiliation: School of Science, Dalian Maritime University, Dalian, 116026, People’s Republic of China
- MR Author ID: 1103537
- Email: ylyang@dlmu.edu.cn
**Deyan Zhang**- Affiliation: School of Mathematical Sciences, Huaibei Normal University, Huaibei, 235000, People’s Republic of China
- MR Author ID: 794578
- Email: zhangdy8005@126.com
- Received by editor(s): November 6, 2016
- Received by editor(s) in revised form: August 22, 2018
- Published electronically: June 27, 2019
- Additional Notes: The first author was supported in part by the Doctoral Scientific Research Foundation of Liaoning Province (No. 20170520382) and the Fundamental Research Funds for the Central Universities (No. 3132017046).

The second author is the corresponding author and was supported in part by the National Natural Science Foundation of China (Nos. 11671298, 11561020) and was partly supported by the Key Project of Natural Science Research in Anhui Province (No. KJ2016A635). - Communicated by: Deane Yang
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 4465-4475 - MSC (2010): Primary 52A40; Secondary 52A15
- DOI: https://doi.org/10.1090/proc/14366
- MathSciNet review: 4002556