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Annular solutions to the partitioning problem in a ball

  • Alberto Cerezo , Isabel Fernández and Pablo Mira EMAIL logo
Published/Copyright: August 28, 2025

Abstract

For any n N , n 2 , we construct a real analytic, one-parameter family of compact embedded CMC annuli with free boundary in the unit ball B 3 of R 3 with a prismatic symmetry group of order 4 n . 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.

Award Identifier / Grant number: PID2020-118137GB-I00

Award Identifier / Grant number: CEX2024-001517-M

Funding source: Fundación Séneca

Award Identifier / Grant number: 21937/PI/22

Funding statement: This research has been financially supported by Project PID2020-118137GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by ESF+; the “Maria de Maeztu” Unit of Excellence IMUS, reference CEX2024-001517-M; and CARM, Programa Regional de Fomento de la Investigación, Fundación Séneca – Agencia de Ciencia y Tecnología Región de Murcia, reference 21937/PI/22.

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Received: 2023-03-24
Published Online: 2025-08-28

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