We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Every noncompact surface is a leaf of a minimal foliation.
- Authors
Gusmão, Paulo; Cotón, Carlos Meniño
- Abstract
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.
- Subjects
FOLIATIONS (Mathematics); RIEMANNIAN metric; MINIMAL surfaces; EULER number; TORUS; TOPOLOGY
- Publication
Revista Mathematica Iberoamericana, 2024, Vol 40, Issue 4, p1207
- ISSN
0213-2230
- Publication type
Article
- DOI
10.4171/RMI/1486