Multiply connected minimal surfaces and the geometric annulus theorem

Nobumitsu NAKAUCHI

doi:10.2969/jmsj/03710017

Nobumitsu NAKAUCHI

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JOURNAL FREE ACCESS

1985 Volume 37 Issue 1 Pages 17-39

DOI https://doi.org/10.2969/jmsj/03710017

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Published: 1985 Received: August 29, 1983 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. W. Cannon and C. D. Feustel, Essential embeddings of annuli and Möbius bands in 3-manifolds, Trans. Amer. Math. Soc., 215 (1976), 219-239.
2) R. Courant, Dirichlet's Principle, Conformal Mapping and Minimal Surfaces, Interscience, New York, 1960.
3) M. Freedman, J. Hass and P. Scott, Least area incompressible surfaces in 3-manifolds, Invent. Math., 71 (1983), 609-642.
4) A. Friedman, Partial Differential Equations, R. E. Krieger Publishing Company, New York, 1969.
5) R. D. Gulliver, R. Osserman and H. L. Royden, A theory of branched immersions of surfaces, Amer. J. Math., 95 (1973), 750-812.
6) W. H. Jaco, Lectures on Three-manifold Topology, Amer. Math. Soc., Providence, 1980.
7) W. Jäger, Behavior of minimal surfaces with free boundaries, Comm. Pure Appl. Math., 23 (1970), 803-818.
8) T. Kobayashi, Equivariant annulus theorem for 3-manifolds, Proc. Japan Acad., 59 (1983), 403-406.
9) W. H. Meeks and S. T. Yau, The classical Plateau problem and the topology of three-dimensional manifolds, Topology, 21 (1982), 409-442.
10) W. H. Meeks and S. T. Yau, Topology of three dimensional manifolds and the embedding problems in minimal surface theory, Ann. of Math., 112 (1980), 441-484.
11) W. H. Meeks and S. T. Yau, The equivariant Dehn's lemma and loop theorem, Comm. Math. Helv., 56 (1981), 225-239.
12) W. H. Meeks and S. T. Yau, The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z., 179 (1982), 151-168.
13) C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York, 1966.
14) R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature, Ann. of Math., 110 (1979), 127-142.
15) F. Waldhausen, On the determination of some bounded 3-manifolds by their fundamental groups alone. In: Proceeding of International Symposium on Topology and its Applications, 331-332. Herceg-Novi, 1968.

Right : [1] J. W. Cannon and C. D. Feustel, Essential embeddings of annuli and Möbius bands in 3-manifolds, Trans. Amer. Math. Soc., 215 (1976), 219-239.
[2] R. Courant, Dirichlet's Principle, Conformal Mapping and Minimal Surfaces, Interscience, New York, 1960.
[3] M. Freedman, J. Hass and P. Scott, Least area incompressible surfaces in 3-manifolds, Invent. Math., 71 (1983), 609-642.
[4] A. Friedman, Partial Differential Equations, R. E. Krieger Publishing Company, New York, 1969.
[5] R. D. Gulliver, R. Osserman and H. L. Royden, A theory of branched immersions of surfaces, Amer. J. Math., 95 (1973), 750-812.
[6] W. H. Jaco, Lectures on Three-manifold Topology, Amer. Math. Soc., Providence, 1980.
[7] W. Jäger, Behavior of minimal surfaces with free boundaries, Comm. Pure Appl. Math., 23 (1970), 803-818.
[8] T. Kobayashi, Equivariant annulus theorem for 3-manifolds, Proc. Japan Acad., 59 (1983), 403-406.
[9] W. H. Meeks and S. T. Yau, The classical Plateau problem and the topology of three-dimensional manifolds, Topology, 21 (1982), 409-442.
[10] W. H. Meeks and S. T. Yau, Topology of three dimensional manifolds and the embedding problems in minimal surface theory, Ann. of Math., 112 (1980), 441-484.
[11] W. H. Meeks and S. T. Yau, The equivariant Dehn's lemma and loop theorem, Comm. Math. Helv., 56 (1981), 225-239.
[12] W. H. Meeks and S. T. Yau, The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z., 179 (1982), 151-168.
[13] C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York, 1966.
[14] R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature, Ann. of Math., 110 (1979), 127-142.
[15] F. Waldhausen, On the determination of some bounded 3-manifolds by their fundamental groups alone. In: Proceeding of International Symposium on Topology and its Applications, 331-332. Herceg-Novi, 1968.

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