Abstract
We show that the critical catenoid, as a free boundary minimal surface of the unit ball in \(\mathbb {R}^3\), has index 4. We also prove that a free boundary minimal surface of the unit ball in \(\mathbb {R}^3\), that is not a flat disk, has index at least 4.
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Acknowledgements
The author is thankful to A. Fraser for introducing him to this problem, as well as for many interesting discussions. What is more, all the results contained in Sects. 6 and 7 of this paper have been obtained in collaboration with A. Fraser. During the time this research was carried out, the author was partially supported by the Natural Sciences and Engineering Research Council of Canada through a post-doctoral fellowship.
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Devyver, B. Index of the critical catenoid. Geom Dedicata 199, 355–371 (2019). https://doi.org/10.1007/s10711-018-0353-2
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DOI: https://doi.org/10.1007/s10711-018-0353-2