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arXiv · 2609.03424

Catenoid-sharp index-topology estimates for minimal hypersurfaces

Junzhang Li
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Abstract

We show that for an embedded two-sided minimal hypersurface in $\mathbb{R}^N$, there is a lower bound for the index in terms of the first Betti number and the number of ends, using ideas from the recent work of Chodosh--Gianocca. This estimate is sharp for the higher-dimensional catenoid. We also obtain a $\operatorname{Spin}(7)$ analogue of Theorem 10.1 of Chodosh--Gianocca: a complete two-sided minimal immersion $M^7\to\mathbb{R}^8$ of index one and finite total curvature is a higher-dimensional catenoid.

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Junzhang Li. 2026-09-03. Catenoid-sharp index-topology estimates for minimal hypersurfaces. https://arxiv.org/abs/2609.03424

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