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Free boundary minimal hypersurfaces of Morse index one in Eucildean half-space
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.
Related
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BibTeX
@misc{li2026free,
title = {{Free boundary minimal hypersurfaces of Morse index one in Eucildean half-space}},
author = {Junzhang Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28824},
eprint = {2610.28824},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28824},
}
RIS
TY - UNPB
TI - Free boundary minimal hypersurfaces of Morse index one in Eucildean half-space
AU - Junzhang Li
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28824
UR - https://arxiv.org/abs/2610.28824
AB - 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.
ER -