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A note on starshaped hypersurfaces with almost constant mean curvature in space forms

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Abstract

We show that closed starshaped hypersurfaces of space forms with almost constant mean curvature or almost constant higher order mean curvature are close to geodesic spheres.

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Acknowledgements

The second author gratefully acknowledges the financial support from the Indian Institute of Technology Goa through Start-up Grant (2021/SG/AU/043).

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Authors and Affiliations

  1. Université Gustave Eiffel, CNRS, LAMA UMR 8050, 77447, Marne-la-Vallée, France

    Julien Roth

  2. School of Mathematics and Computer Science, Indian Institute of Technology, Goa, 403401, India

    Abhitosh Upadhyay

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  1. Julien Roth
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  2. Abhitosh Upadhyay
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Correspondence to Abhitosh Upadhyay.

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Roth, J., Upadhyay, A. A note on starshaped hypersurfaces with almost constant mean curvature in space forms. Arch. Math. 122, 109–120 (2024). https://doi.org/10.1007/s00013-023-01932-4

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  • DOI: https://doi.org/10.1007/s00013-023-01932-4

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