Free boundary minimal hypersurfaces outside of the ball

• Laurent Mazet ^[2] ; Abraão Mendes ^[1]
  1. [1] Universidade Federal de Alagoas

     Universidade Federal de Alagoas

     Brasil

     
  2. [2] Université de Tours, France
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 1, 2024, págs. 277-298
• Idioma: inglés
• DOI: 10.4171/RMI/1453
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• Resumen

  • In this paper, we obtain two classification theorems for free boundary minimal hypersurfaces outside of the unit ball (exterior FBMH, for short) in Euclidean space. The first result states that the only exterior stable FBMH with parallel embedded regular ends are the catenoidal hypersurfaces. To achieve this, we prove a Bôcher-type result for positive Jacobi functions on regular minimal ends in R n+1 that, after some calculations, implies the first theorem. The second theorem states that any exterior FBMH Σ with one regular end is a catenoidal hypersurface. Its proof is based on a symmetrization procedure similar to that of R. Schoen. We also give a complete description of the catenoidal hypersurfaces, including the calculation of their indices.