A note on new weighted geometric inequalities for hypersurfaces in $\mathbb {R}^n$
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- by Jie Wu;
- Proc. Amer. Math. Soc. 152 (2024), 4049-4056
- DOI: https://doi.org/10.1090/proc/16875
- Published electronically: July 17, 2024
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Abstract:
In this note, we prove a family of sharp weighed inequalities which involve weighted $k$-th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in $\mathbb {R}^n$. This inequality generalizes the corresponding result of Wei and Zhou [Bull. Lond. Math. Soc. 55 (2023), pp. 263–281] where their proof is based on earlier results of Kwong-Miao [Pacific J. Math. 267 (2014), pp. 417–422; Commun. Contemp. Math. 17 (2015), p. 1550014]. Here we present a proof which does not rely on Kwong-Miao’s results.References
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Bibliographic Information
- Jie Wu
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
- Email: wujiewj@zju.edu.cn
- Received by editor(s): November 30, 2023
- Received by editor(s) in revised form: March 1, 2024
- Published electronically: July 17, 2024
- Additional Notes: This work was supported by the National Key R$\&$D Program of China Grant 2022YFA1005500 and National Science Foundation of China under Grant No. 11731001.
- Communicated by: Jiaping Wang
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 4049-4056
- MSC (2020): Primary 53C21; Secondary 53A07
- DOI: https://doi.org/10.1090/proc/16875
- MathSciNet review: 4781994