Uniqueness of area minimizing surfaces for extreme curves

• Autores: Baris Coskunuzer, Tolga Etgü
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 30, Nº 4, 2014, págs. 1135-1148
• Idioma: inglés
• DOI: 10.4171/RMI/810
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• Resumen

  • Let M be a compact, orientable, mean convex 3-manifold with boundary ∂M. We show that the set of all simple closed curves in ∂M which bound unique area minimizing disks in M is dense in the space of simple closed curves in ∂M which are nullhomotopic in M. We also show that the set of all simple closed curves in ∂M which bound unique absolutely area minimizing surfaces in M is dense in the space of simple closed curves in ∂M which are nullhomologous in M.