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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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