Journal of Differential Geometry

Boundary slopes of immersed surfaces in 3-manifolds

Joel Hass, J. Hyam Rubinstein, and Shicheng Wang

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 52, Number 2 (1999), 303-325.

Dates
First available in Project Euclid: 25 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214425279

Digital Object Identifier
doi:10.4310/jdg/1214425279

Mathematical Reviews number (MathSciNet)
MR1758298

Zentralblatt MATH identifier
0978.57016

Subjects
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M50: Geometric structures on low-dimensional manifolds

Citation

Hass, Joel; Rubinstein, J. Hyam; Wang, Shicheng. Boundary slopes of immersed surfaces in 3-manifolds. J. Differential Geom. 52 (1999), no. 2, 303--325. doi:10.4310/jdg/1214425279. https://projecteuclid.org/euclid.jdg/1214425279


Export citation

References

  • [1] C. Adams, The non-compact hyperbolic S-manifold of minimum volume, Proc. Amer. Math. Soc. 100 (1987) 601-106.
  • [2] C. Adams, Volumes of N-cusped hyperbolic 3-manifolds, J. London Math. Soc. 38 (1988) 555-565.
  • [3] I. Agol, Bounds on exceptional Dehn filling, math.GT/9906183.
  • [4] T. M. Apostol, Introduction to analytic number theory, Springer, Berlin, 1976.
  • [5] M. Baker, On boundary slopes of immersed incompressible surfaces, Ann. Inst. Fourier (Grenoble) 46 (1996) 1443-1449.
  • [6] S. Bleiler and C. Hodgson, Spherical space forms and Dehn filling, Topology 35 (1996) 809-833.
  • [7] M. Freedman, J. Hass and P. Scott, least area incompressible surfaces in 3-manifolds, Invent. Math. 71 (1983) 609-642.
  • [8] C. Gordon, Dehn surgery on knots, Proc. ICM Kyoto, Springer, Berlin, 1990, 631-642.
  • [9] C. Gordon and R. Litherland, Incompressible planar surfaces in 3-manifolds, Topology Appl. 18 (1984) 121-144.
  • [10] M. Gromov and W. Thurston, Pinching constants for hyperbolic 3-manifolds, Invent. Math. 89 (1987) 1-12.
  • [11] J. Hass, Minimal surfaces in manifolds with S1 actions and the simple loop conjecture for Seifert fiber spaces, Proc. Amer. Math. Soc. 99 (1987) 383-388.
  • [12] J. Hass and P. Scott, The existence of least area surfaces in 3-manifolds, Trans. Amer. Math. Soc. 310 (1988) 87-114.
  • [13] A. Hatcher, On the boundary curves of incompressible surfaces, Pacific J. Math. 99 (1982) 373-377.
  • [14] M. Lackenby, Word hyperbolic Dehn surgery, math.GT/980812, to appear in Invent. Math.
  • [15] B. Leeb, 3-manifolds with(out) metrics of nonpositive curvature, Invent. Math. 122 (1995) 277-289.
  • [16] J. Luecke, Dehn surgery on knots %n S3, Proc. ICM Zurich(1994) 585-594.
  • [17] J. Luecke, Dehn surgery on knots %n S3, Amer. Math. Soc. Abstracts 17, 434.
  • [18] U. Oertel, Boundaries of 7Ti -injective surfaces, Topology Appl. 78 (1997) 215-234.
  • [19] J. H. Rubinstein and S. C. Wang, ni-injective surfaces in graph manifolds, Comment. Math. Helv. 73 (1998) 499-515.
  • [20] D. Ruberman, Mutation and volumes of knots in S3, Invent. Math. 90 (1987) 189-215.
  • [21] P. Shalen, Representations of 3-manifold groups and its application to topology, Proc. ICM Berkeley, 1986, 607-614.
  • [22] R. Schoen, Estimates for stable minimal surfaces in three dimensional manifolds, Seminar on minimal submanifolds, (ed. E. Bombieri), Princeton Univ. Press, 1983, 111-126.
  • [23] R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of S-dimensional manifolds with non-negative scalar curvature, Ann. of Math. 110 (1979) 127-142.
  • [24] W. Thurston, Geometry and topology of S-manifolds, Princeton Lecture Notes, Princeton, NJ, 1978.
  • [25] J. Maher, Virtually embedded boundary slopes, Topology Appl. 95 (1999) no. 1, 63-74.
  • [26] C. Cao and R. Meyerhoff, The orientable cusped hyperbolic S-manifolds of minimal volume, Preprint.