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First \(\frac{2}{n}\)-stability eigenvalue of singular minimal hypersurfaces in space forms

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Abstract

In this paper, we study the first \(\frac{2}{n}\)-stability eigenvalue on singular minimal hypersurfaces in space forms. We provide a characterization of catenoids in space forms in terms of \(\frac{2}{n}\)-stable eigenvalue. We emphasize that this result is even new in the regular setting.

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Acknowledgements

This work is completed during a stay of the first two authors (H. T. Dung and N. T. Dung) at the Vietnam Institutes for Advanced Study in Mathematics (VIASM). They would like to express their thanks to the staff there for support. The first author (H. T. Dung) was funded by Vingroup JSC and supported by the PhD Scholarship Program of Vingroup Innovation Foundation (VINIF), Institute of Big Data, code VINIF.2021.TS.010. H. T. Dung also was funded by Hanoi Pedagogical University 2 Foundation for Sciences and Technology Development via grant number C.2020-SP2-07. The third author (J. Pyo) was supported by the National Research Foundation of Korea (NRF-2020R1A2C1A01005698 and NRF-2021R1A4A1032418).

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Authors and Affiliations

  1. Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam

    Ha Tuan Dung

  2. Faculty of Mathematics - Mechanics - Informatics, Vietnam National University, University of Science, Hanoi, Hanoi, Vietnam

    Nguyen Thac Dung

  3. Thang Long Institute of Mathematics and Applied Sciences (TIMAS), Thang Long University, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam

    Nguyen Thac Dung

  4. Department of Mathematics, Pusan National University, Busan, Korea

    Juncheol Pyo

  5. Korea Institute for Advanced Study, Seoul, 02455, Korea

    Juncheol Pyo

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  1. Ha Tuan Dung
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  2. Nguyen Thac Dung
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  3. Juncheol Pyo
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Correspondence to Juncheol Pyo.

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Dung, H.T., Dung, N.T. & Pyo, J. First \(\frac{2}{n}\)-stability eigenvalue of singular minimal hypersurfaces in space forms. Ann Glob Anal Geom 63, 1 (2023). https://doi.org/10.1007/s10455-022-09880-y

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  • DOI: https://doi.org/10.1007/s10455-022-09880-y

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