Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Authors: Yunlong Yang and Deyan Zhang
Journal: Proc. Amer. Math. Soc. 147 (2019), 4465-4475
MSC (2010): Primary 52A40; Secondary 52A15
DOI: https://doi.org/10.1090/proc/14366
Published electronically: June 27, 2019
MathSciNet review: 4002556
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 52A40, 52A15

Retrieve articles in all journals with MSC (2010): 52A40, 52A15


Additional Information

Yunlong Yang
Affiliation: School of Science, Dalian Maritime University, Dalian, 116026, People’s Republic of China
Email: ylyang@dlmu.edu.cn

Deyan Zhang
Affiliation: School of Mathematical Sciences, Huaibei Normal University, Huaibei, 235000, People’s Republic of China
Email: zhangdy8005@126.com

DOI: https://doi.org/10.1090/proc/14366
Keywords: Cone-volume measure, constant width bodies, log-Brunn-Minkowski's inequality, log-Minkowski's inequality, $L_p$-Brunn-Minkowski's inequality, $L_p$-Minkowski inequality, $\mathfrak{R}_i$ class.
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
Article copyright: © Copyright 2019 American Mathematical Society