Skip to main content

Minimal branched immersions into three-manifolds

Part of the Lecture Notes in Mathematics book series (LNM,volume 1167)

Keywords

  • Riemann Surface
  • Minimal Surface
  • Homotopy Class
  • Positive Scalar Curvature
  • Minimal Immersion

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.F. Atiyah, Geometry of monopoles. Monopole Conf. ICTP (1981), 3–20.

    Google Scholar 

  2. P. Baird and J. Eells, A conservation law for harmonic maps. Geom. Symp. Utrecht (1980). Springer Notes 894 (1981), 1–15.

    Google Scholar 

  3. M.J. Beeson, On interior branch points of minimal surfaces. Math. Z. 171 (1980), 133–154.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. J. Eells, Gauss maps of surfaces. Oberwolfach Volume 1944–1984.

    Google Scholar 

  5. J. Eells and L. Lemaire, A report on harmonic maps. Bull. London Math. Soc. 10 (1978), 1–68.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. J. Eells and S. Salamon, Constructions twistorielles des applications harmoniques. C.R. Acad. Paris I 296 (1983), 685–687.

    MathSciNet  MATH  Google Scholar 

  7. J. Eells and S. Salamon, Twistorial construction of harmonic maps of surfaces into four-manifolds. (To appear).

    Google Scholar 

  8. J. Eells and J.H. Sampson, Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86 (1964), 109–160.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. M. Freedman, J. Hass, and P. Scott, Least area incompressible surfaces in 3-manifolds. Inv. Math. 71 (1983), 601–642.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. M. Gromov and H.B. Lawson, Spin and scalar curvature in the presence of a fundamental group. I. Ann. Math. 111 (1980), 209–230.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. M. Gromov and H.B. Lawson, The classification of simply connected manifolds of positive scalar curvature. Ann. Math. 111 (1980), 423–434.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. R.D. Gulliver, Regularity of minimizing surfaces of prescribed mean curvature. Ann. Math. 97 (1973), 275–305.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. R.D. Gulliver, R. Osserman, and H.L. Royden, A theory of branched immersions of surface. Amer. J. Math. 95 (1973), 750–812.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. P. Hall, Regular homotopies of branched immersions.

    Google Scholar 

  15. R. Hamilton, Three-manifolds with positive Ricci curvature. J. Diff. Geo. 17 (1982), 255–306.

    MathSciNet  MATH  Google Scholar 

  16. J. Hass and J. Hughes, Immersions of surfaces in 3-manifolds.

    Google Scholar 

  17. J. Hempel, 3-manifolds. Ann. Math. Studies 86 (1976).

    Google Scholar 

  18. M. Hirsch, Immersions of manifolds. Trans. Amer. Math. Soc. 93 (1959), 242–276.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. N.J. Hitchin, Monopoles and geodesics. Comm. Math. Phys. 83 (1982), 579–602.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. H.B. Lawson, Complete minimal surfaces in S3, Ann. Math. 92 (1970), 335–374.

    CrossRef  MATH  Google Scholar 

  21. C.R. Lebrun, The imbedding problem for twistor CR manifolds.

    Google Scholar 

  22. W.H. Meeks, The conformal structure and geometry of triply periodic minimal surfaces in 3. Thesis, Berkeley (1975).

    Google Scholar 

  23. W.H. Meeks and S.-T. Yau, Topology of three dimensional manifolds and the embedding problems in minimal surface theory. Ann. Math. 112 (1980), 441–484.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. W. H. Meeks and S.-T. Yau, The classical Plateau problem and the topology of three dimensional manifolds. Topology 21 (1982), 408–442.

    CrossRef  MathSciNet  Google Scholar 

  25. W.H. Meeks and S.-T. Yau, The existence of embedded minimal surfaces and the problem of uniqueness. Math. Z. 179 (1982), 151–168.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. W.H. Meeks, L. Simon, and S.-T. Yau, Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature. Ann. Math. 116 (1982), 621–659.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. R. Osserman, A proof of the regularity everywhere of the classical solution to Plateau's problem. Ann. Math. 91 (1970), 550–569.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. N.C. Papakyriakopoulos, On Dehn's lemma and the asphericity of knots. Ann. Math. 66 (1957), 1–26.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. J.T. Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds. Princeton Notes Series 27 (1981).

    Google Scholar 

  30. J. Sacks and K. Uhlenbeck, Minimal immersions of closed Riemann surfaces, Trans. Amer. Math. Soc. 271 (1982), 639–652.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. J.H. Sampson, Some properties and applications of harmonic mappings. Ann. Ec. Norm. Sup. XI (1978), 221–228.

    MathSciNet  MATH  Google Scholar 

  32. A. Sanini, Applicazioni tra varietà riemanniane con energia critica rispetto a deformazioni di metriche. Rend-Mat. 3 (1983) Ser. VII, 53–63.

    MathSciNet  MATH  Google Scholar 

  33. R. Schoen and S.-T. Yau, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature. Ann. Math. 110 (1979), 127–142.

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. P. Scott, The geometries of 3-manifolds. Bull. London Math. Soc. 15 (1983), 401–487.

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. S. Smale, A survey of some recent developments in differential topology. Bull. Amer. Math. Soc. 69 (1963), 131–145.

    CrossRef  MathSciNet  MATH  Google Scholar 

  36. F.R. Smith, On the existence of embedded minimal 2-spheres in the 3-sphere, endowed with an arbitrary metric. Thesis, Melbourne (1982).

    Google Scholar 

  37. K. Uhlenbeck, Closed minimal surfaces in hyperbolic 3-manifolds. Ann. Math. Studies 103, (1983), 147–168.

    MathSciNet  MATH  Google Scholar 

  38. S.-T. Yau, Minimal surfaces and their role in differential geometry. E. Horwood Series (1984), 99–103.

    Google Scholar 

  39. H.I. Choi and R. Schoen, The space of minimal embeddings of a surface into a three — dimensional manifold of positive Ricci curvature.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Eells, J. (1985). Minimal branched immersions into three-manifolds. In: Geometry and Topology. Lecture Notes in Mathematics, vol 1167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075217

Download citation

  • DOI: https://doi.org/10.1007/BFb0075217

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16053-3

  • Online ISBN: 978-3-540-39738-0

  • eBook Packages: Springer Book Archive