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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The logarithmic Minkowski inequality for cylinders
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by Jiangyan Tao, Ge Xiong and Jiawei Xiong
Proc. Amer. Math. Soc. 151 (2023), 2143-2154
DOI: https://doi.org/10.1090/proc/16307
Published electronically: February 17, 2023

Abstract:

In this paper, we prove that if $K$ is an $o$-symmetric cylinder and $L$ is an $o$-symmetric convex body in $\mathbb R^3$, then the logarithmic Minkowski inequality \[ \frac {1}{V(K)}\int _{\mathbb S^{2}}\log \frac {h_L}{h_K}\,dV_K\geq \frac {1}{3}\log \frac {V(L)}{V(K)} \] holds, with equality if and only if $K$ and $L$ are relative cylinders.
References
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Bibliographic Information
  • Jiangyan Tao
  • Affiliation: School of Mathematical Sciences, Tongji University, Shanghai 200092, People’s Republic of China
  • ORCID: 0000-0001-7998-3879
  • Email: 2010534@tongji.edu.cn
  • Ge Xiong
  • Affiliation: School of Mathematical Sciences, Tongji University, Shanghai 200092, People’s Republic of China
  • Email: xiongge@tongji.edu.cn
  • Jiawei Xiong
  • Affiliation: School of Mathematics and Statistics, Ningbo University, Ningbo 315211, People’s Republic of China
  • ORCID: 0000-0002-4298-9764
  • Email: xiongjiawei@nbu.edu.cn
  • Received by editor(s): May 6, 2022
  • Received by editor(s) in revised form: September 9, 2022, and September 20, 2022
  • Published electronically: February 17, 2023
  • Additional Notes: Research of the authors was supported by NSFC No. 12271407.
  • Communicated by: Gaoyang Zhang
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 2143-2154
  • MSC (2020): Primary 28A75, 52A40, 49Q15
  • DOI: https://doi.org/10.1090/proc/16307
  • MathSciNet review: 4556207