Abstract For any n ∈ N n, n ≥ 2 n 2, we construct a real analytic, one-parameter family of compact embedded CMC annuli with free boundary in the unit ball B 3 B^3 of R 3 R^3 with a prismatic symmetry group of order 4 n 4n. These examples give a negative answer to the uniqueness problem by Nitsche and Wente of whether any annular solution to the partitioning problem in the ball should be rotational.
Cerezo et al. (Wed,) studied this question.