First stability eigenvalue of singular hypersurfaces with constant mean curvature in the unit sphere
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- by Nguyen Thac Dung, Juncheol Pyo and Hung Tran
- Proc. Amer. Math. Soc. 151 (2023), 795-810
- DOI: https://doi.org/10.1090/proc/16120
- Published electronically: August 19, 2022
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Abstract:
In this paper, we study the first eigenvalue of the stability operator on an integral $n$-varifold with constant mean curvature in the unit sphere $\mathbb {S}^{n+1}$. We find the optimal upper bound and prove a rigidity result characterizing the case when it is attained. This gives a new characterization for certain singular Clifford tori.References
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Bibliographic Information
- Nguyen Thac Dung
- Affiliation: Department of Mathematics, Vietnam National University, University of Science, Hanoi, Vietnam, and Thang Long Institute of Mathematics and Applied Sciences (TIMAS), Thang Long University, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam
- MR Author ID: 772632
- Email: dungmath@gmail.com, dungmath@vnu.edu.vn
- Juncheol Pyo
- Affiliation: Department of Mathematics, Pusan National University, Korea
- MR Author ID: 896125
- ORCID: 0000-0002-5153-0621
- Email: jcpyo@pusan.ac.kr
- Hung Tran
- Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79413
- MR Author ID: 899959
- Email: hungtran@ttu.edu.us
- Received by editor(s): September 28, 2021
- Received by editor(s) in revised form: September 29, 2021, January 29, 2022, March 15, 2022, and April 17, 2022
- Published electronically: August 19, 2022
- Additional Notes: The second author was supported by the National Research Foundation of Korea (NRF-2020R1A2C1A01005698 and NRF-2021R1A4A1032418). The third author was partially supported by a Simons Foundation Collaboration Grant and NSF grant DMS-2104988.
The second author is the corresponding author. - Communicated by: Guofang Wei
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 795-810
- MSC (2020): Primary 53C24; Secondary 53C42
- DOI: https://doi.org/10.1090/proc/16120
- MathSciNet review: 4520028