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
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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