Abstract
In this paper, we prove that a flat free boundary minimal n-disk, \(n\ge 3\), in the unit Euclidean ball \({\mathbb {B}}^{n+1}\) is the unique compact free boundary minimal hypersurface whose squared norm of the second fundamental form is less than either \(\frac{n^2}{4}\) or \(\frac{(n-2)^2}{4|x|^2}\). Moreover, we prove analogous results for compact free boundary minimal hypersurfaces in annular domains or balls with a conformally Euclidean metric.
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Acknowledgements
The authors would like to thank the referees for their valuable suggestions and comments which made this paper better and more concise. The authors were partially supported respectively by CNPq, FAPEMIG and CAPES/Brazil agencies grants.
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Barbosa, E., Gonçalves, R.A. & Pereira, E. Uniqueness Results for Free Boundary Minimal Hypersurfaces in Conformally Euclidean Balls and Annular Domains. J Geom Anal 31, 9800–9818 (2021). https://doi.org/10.1007/s12220-021-00628-x
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DOI: https://doi.org/10.1007/s12220-021-00628-x