Free boundary minimal annuli in convex balls

@misc{ko2026free,
  title = {{Free boundary minimal annuli in convex balls}},
  author = {Dongyeong Ko and Guanhua Shao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.14679},
  eprint = {2608.14679},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.14679},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Free boundary minimal annuli in convex balls
AU  - Dongyeong Ko
AU  - Guanhua Shao
PY  - 2026
DA  - 2026/10/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.14679
UR  - https://arxiv.org/abs/2608.14679
AB  - We construct a $4$-parameter family of properly embedded genus-zero surfaces with at most two boundary components in a Riemannian $3$-ball. The construction is a free boundary analog of the canonical $5$-parameter family of surfaces on the $3$-sphere by Marques-Neves in the proof of Willmore conjecture. In the Euclidean unit ball, this family realizes the critical catenoid as a Simon-Smith min-max limit. As applications, we give an upper bound of Almgren-Pitts $4$-width ω_4(𝔹^3) by the area of the critical catenoid. Moreover, we prove the existence of at least three free boundary minimal annuli in any compact $3$-manifold with nonnegative Ricci curvature and strictly convex boundary.
ER  -