Annular solutions to the partitioning problem in a ball

Key Points

• Constructed a family of compact embedded CMC annuli demonstrates the complexity of the partitioning problem.
• These annular solutions show a negative answer to the uniqueness problem posed by Nitsche and Wente.
• The solutions have a prismatic symmetry group with an order of 4n, affecting their geometric properties.
• The findings challenge existing assumptions about rotational symmetry in partitioning solutions.

Abstract