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arXiv · 2610.24878

Index-one capillary minimal hypersurfaces in \(\mathbb R^n_+\)

Chenghang Lu
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Abstract

We classify complete, two-sided, properly embedded capillary minimal surfaces with nonempty boundary and Morse index one in \(\mathbb R^3_+\). More precisely, if the boundary is compact, these surfaces are catenoid truncations; if the boundary is noncompact, they are capillary hairpin surfaces. The classification extends to higher dimensions under extrinsic Euclidean volume growth and Wang--Zhang's dimension and angle conditions.

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Chenghang Lu. 2026-10-17. Index-one capillary minimal hypersurfaces in \(\mathbb R^n_+\). https://arxiv.org/abs/2610.24878

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