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
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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