PreprintarXiv licencearXiv
Index-one capillary minimal hypersurfaces in ℝn+
Abstract
We classify complete, two-sided, properly embedded capillary minimal surfaces with nonempty boundary and Morse index one in ℝ3+. 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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BibTeX
@misc{lu2026indexone,
title = {{Index-one capillary minimal hypersurfaces in \(\mathbb R^n_+\)}},
author = {Chenghang Lu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24878},
eprint = {2610.24878},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24878},
}
RIS
TY - UNPB
TI - Index-one capillary minimal hypersurfaces in ℝ^n_+
AU - Chenghang Lu
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24878
UR - https://arxiv.org/abs/2610.24878
AB - We classify complete, two-sided, properly embedded capillary minimal surfaces with nonempty boundary and Morse index one in 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.
ER -