PreprintCC BY 4.0arXiv
Conformally flat free boundary minimal hypersurfaces in the ball
Abstract
In this note, we show that a locally conformally flat free boundary minimal hypersurface in Bn must be either an equatorial ball or a critical catenoid for all n ≥ 4. As a consequence, we conclude that the equatorial ball is unique among locally conformally flat free boundary minimal hypersurfaces in Bn with the topology of Bn − 1.
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BibTeX
@misc{santos2026conformally,
title = {{Conformally flat free boundary minimal hypersurfaces in the ball}},
author = {Roney Santos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11779},
eprint = {2610.11779},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11779},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Conformally flat free boundary minimal hypersurfaces in the ball
AU - Roney Santos
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11779
UR - https://arxiv.org/abs/2610.11779
AB - In this note, we show that a locally conformally flat free boundary minimal hypersurface in B^n must be either an equatorial ball or a critical catenoid for all n ≥ 4. As a consequence, we conclude that the equatorial ball is unique among locally conformally flat free boundary minimal hypersurfaces in B^n with the topology of B^n − 1.
ER -