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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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One dimensional $\mathsf {RCD}$ spaces always satisfy the regular Weyl’s law
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by Akemi Iwahashi, Yu Kitabeppu and Akari Yonekura
Proc. Amer. Math. Soc. 151 (2023), 4923-4934
DOI: https://doi.org/10.1090/proc/16477
Published electronically: July 28, 2023

Abstract:

Ambrosio, Honda, and Tewodrose proved that the regular Weyl’s law is equivalent to a mild condition related to the infinitesimal behavior of the measure of balls in compact finite dimensional $\mathsf {RCD}$ spaces. Though that condition is seemed to always hold for any such spaces, however, Dai, Honda, Pan, and Wei recently showed that for any integer $n$ at least 2, there exists a compact $\mathsf {RCD}$ space of $n$ dimension fails to satisfy the regular Weyl’s law. In this short article we prove that one dimensional $\mathsf {RCD}$ spaces always satisfy the regular Weyl’s law.
References
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Bibliographic Information
  • Akemi Iwahashi
  • Affiliation: Graduate School of Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan
  • Email: akeminiwa4@yahoo.com
  • Yu Kitabeppu
  • Affiliation: Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan
  • MR Author ID: 1055218
  • ORCID: 0000-0002-5043-841X
  • Email: ybeppu@kumamoto-u.ac.jp
  • Akari Yonekura
  • Affiliation: Graduate School of Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan
  • Email: a.yonekura.mm@gmail.com
  • Received by editor(s): February 18, 2023
  • Received by editor(s) in revised form: February 26, 2023
  • Published electronically: July 28, 2023
  • Additional Notes: The second author was partly supported by JSPS KAKENHI Grant Numbers JP18K13412 and JP22K03291.
  • Communicated by: Jiaping Wang
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4923-4934
  • MSC (2020): Primary 51F99
  • DOI: https://doi.org/10.1090/proc/16477
  • MathSciNet review: 4634893