Sufficient symmetry conditions for free boundary minimal annuli to be the critical catenoid

• Dong-Hwi Seo ^[1]
  1. [1] Seoul National University,Seoul, Republic of Korea
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 3, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-026-01150-0
• Enlaces
  • Texto completo
• Resumen

  • We provide several sufficient symmetry conditions for an embedded free boundary minimal annulus in the unit 3-ball to be congruent to the critical catenoid. First, we show that an annulus with either two symmetry planes or a symmetry plane that does not intersect the boundary must be congruent to the critical catenoid. As a corollary, any embedded free boundary minimal annulus in the half-ball satisfying certain boundary conditions is also the critical catenoid. Building on a symmetry principle, we further show that if the boundary consists of two congruent components and is invariant under reflection through a plane, then the surface is congruent to the critical catenoid.

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