Annular solutions to the partitioning problem in a ball

For any <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>∈</m:mo> <m:mi mathvariant="double-struck">N</m:mi> </m:mrow> </m:math> n , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>≥</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> n≥ 2 , we construct a real analytic, one-parameter family of compact embedded CMC annuli with free boundary in the unit ball <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi mathvariant="double-struck">B</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> B³ of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi mathvariant="double-struck">R</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> R³ with a prismatic symmetry group of order <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>4</m:mn> <m:mo>⁢</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> 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.