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arXiv · 2610.28824

Free boundary minimal hypersurfaces of Morse index one in Eucildean half-space

Junzhang Li
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Abstract

We prove that a complete, connected, two-sided, embedded free boundary minimal hypersurface of finite total curvature and Morse index one in a half-space of RN, with nonempty boundary is a higher-dimensional half-catenoid. We also prove that a complete, connected, two-sided, embedded free boundary minimal hypersurface of finite total curvature and Morse index one in a quarter-space is the higher-dimensional quarter-catenoid.

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Junzhang Li. 2026-10-20. Free boundary minimal hypersurfaces of Morse index one in Eucildean half-space. https://arxiv.org/abs/2610.28824

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