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On the double curves of least area tori


Author: Max Neumann-Coto
Journal: Proc. Amer. Math. Soc. 125 (1997), 2463-2469
MSC (1991): Primary 57M60, 57R45
DOI: https://doi.org/10.1090/S0002-9939-97-04071-9
MathSciNet review: 1415336
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Abstract: The double curves of least area immersions of the torus into closed, orientable, irreducible 3-manifolds are simple in the torus. A related result for other least area surfaces is given.


References [Enhancements On Off] (What's this?)

  • 1. A.Casson, The Torus Theorem, notes from a talk.
  • 2. M.Freedman, J.Hass, P.Scott, Least area incompressible surfaces in 3-manifolds, Invent. Math. 71 (1983), 609-642. MR 85e:57012
  • 3. R.Gulliver, P.Scott Least area surfaces can have excess triple points, Topology 26-3 (1987), 345-359. MR 88k:57018
  • 4. M.Neumann-Coto Least area and minimal intersection of immersed surfaces, in preparation.

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Additional Information

Max Neumann-Coto
Affiliation: Instituto de Matemáticas, UNAM, México D.F. 04510, Mexico
Email: max@math.unam.mx

DOI: https://doi.org/10.1090/S0002-9939-97-04071-9
Keywords: 3-manifolds, immersions, minimal surfaces
Received by editor(s): October 11, 1995
Communicated by: Ronald Stern
Article copyright: © Copyright 1997 American Mathematical Society

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