Uniqueness of free boundary minimal annuli

@misc{parise2026uniqueness,
  title = {{Uniqueness of free boundary minimal annuli}},
  author = {Davide Parise and Jonathan J. Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17512},
  eprint = {2609.17512},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17512},
}

TY  - UNPB
TI  - Uniqueness of free boundary minimal annuli
AU  - Davide Parise
AU  - Jonathan J. Zhu
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17512
UR  - https://arxiv.org/abs/2609.17512
AB  - We prove that every smooth properly embedded free-boundary minimal annulus in the unit ball is congruent to the critical catenoid. We also classify positive solutions of (Δ_𝕊^2+2)u=0 on smooth spherical annuli with u=0 and |∇ u|=1 on the boundary; their one-homogeneous extensions are the axially symmetric Alt-Caffarelli cones. Lastly, we also treat the case of free-boundary minimal annuli in spherical caps.
ER  -