Every noncompact surface is a leaf of a minimal foliation

• Paulo Gusmão ^[1] ; Carlos Meniño Cotón ^[2]
  1. [1] Universidade Federal Fluminense

     Universidade Federal Fluminense

     Brasil

     
  2. [2] Universidade de Vigo

     Universidade de Vigo

     Vigo, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 4, 2024, págs. 1207-1248
• Idioma: inglés
• DOI: 10.4171/RMI/1486
• Enlaces
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• Resumen

  • We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed 3-manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle. Moreover, the above result is also true for any prescription of a countable family of topologies of noncompact surfaces: they can coexist in the same minimal foliation. All the given examples are hyperbolic foliations, meaning that they admit a leafwise Riemannian metric of constant negative curvature. Many oriented Seifert manifolds with a fibered incompressible torus and whose associated orbifold is hyperbolic admit minimal foliations as above. The given examples are not transversely C2 -smoothable.