PreprintCC BY 4.0arXiv
Constant mean curvature disks with circular boundary in the $3$-sphere and in hyperbolic space
Abstract
We prove that a compact immersed disk of constant mean curvature in 𝕊3 or in ℍ3 whose boundary is mapped diffeomorphically onto a circle is an embedded totally umbilical disk.
Related
- Constant mean curvature disks with circular boundary
- Stable constant mean curvature disks with circular boundary in homogeneous three-manifolds
- Hypersurfaces of constant higher order mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity
- Sphere Theorems for Immersed Hypersurfaces with Constant Scalar Curvature
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BibTeX
@misc{lopez2026constant,
title = {{Constant mean curvature disks with circular boundary in the $3$-sphere and in hyperbolic space}},
author = {Rafael López},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39790},
eprint = {2609.39790},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39790},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constant mean curvature disks with circular boundary in the $3$-sphere and in hyperbolic space
AU - Rafael López
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39790
UR - https://arxiv.org/abs/2609.39790
AB - We prove that a compact immersed disk of constant mean curvature in 𝕊^3 or in ℍ^3 whose boundary is mapped diffeomorphically onto a circle is an embedded totally umbilical disk.
ER -