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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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On a relation between the $\mathrm {K}$-cowaist and the $\hat {\mathsf {A}}$-cowaist
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by Xiangsheng Wang
Proc. Amer. Math. Soc. 151 (2023), 4983-4990
DOI: https://doi.org/10.1090/proc/16526
Published electronically: August 22, 2023

Abstract:

The $\mathrm {K}$-cowaist $\mathrm{K-cw}_2(M)$ and the $\hat {\mathsf {A}}$-cowaist $\hat {\mathrm{A}}-\mathrm{cw}_2(M)$ are two interesting invariants on a manifold $M$, which are closely related to the existence of the positive scalar curvature metric on $M$. In this note, we give a detailed proof of the following inequality due to Gromov: $\mathrm{K-cw}_2(M) \le c \hat {\mathrm{A}}-\mathrm{cw}_2(M)$, where $c$ is a dimensional constant.
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Bibliographic Information
  • Xiangsheng Wang
  • Affiliation: Beijing International Center for Mathematical Research, Peking University, Beijing 100871, People’s Republic of China
  • Address at time of publication: School of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China
  • ORCID: 0000-0002-2484-2320
  • Email: xiangsheng@sdu.edu.cn
  • Received by editor(s): February 5, 2022
  • Received by editor(s) in revised form: April 20, 2023, and April 22, 2023
  • Published electronically: August 22, 2023
  • Additional Notes: The author was partially supported by NSFC Grant No. 12101361.
  • Communicated by: Jiaping Wang
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4983-4990
  • MSC (2020): Primary 53C23; Secondary 57R20
  • DOI: https://doi.org/10.1090/proc/16526
  • MathSciNet review: 4634899