The Michigan Mathematical Journal

The structure of stable minimal surfaces near a singularity

William H. Meeks III

Full-text: Open access

Article information

Source
Michigan Math. J., Volume 55, Issue 1 (2007), 155-161.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1177681990

Digital Object Identifier
doi:10.1307/mmj/1177681990

Mathematical Reviews number (MathSciNet)
MR2320177

Zentralblatt MATH identifier
1133.53005

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 49Q05: Minimal surfaces [See also 53A10, 58E12] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Meeks III, William H. The structure of stable minimal surfaces near a singularity. Michigan Math. J. 55 (2007), no. 1, 155--161. doi:10.1307/mmj/1177681990. https://projecteuclid.org/euclid.mmj/1177681990


Export citation

References

  • T. H. Coding and W. P. Minicozzi II, The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus, preprint, math.DG/0509647, 2005.
  • M. do Carmo and C. K. Peng, Stable complete minimal surfaces in $\Bbb R^3$ are planes, Bull. Amer. Math. Soc. 1 (1979), 903--906.
  • D. Fischer-Colbrie and R. Schoen, The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature, Comm. Pure Appl. Math. 33 (1980), 199--211.
  • R. Gulliver and H. B. Lawson, The structure of stable minimal hypersurfaces near a singularity, Geometric measure theory and the calculus of variations (Arcata, 1984), Proc. Sympos. Pure Math., 44, pp. 213--237, Amer. Math. Soc., Providence, RI, 1986.
  • W. H. Meeks III, J. Pérez, and A. Ros, The geometry of minimal surfaces of finite genus II; nonexistence of one limit end examples, Invent. Math 158 (2004), 323--341.
  • ------, Embedded minimal surfaces: Removable singularities, local pictures and parking garage structures, the dynamics of dilation invariant collections and the characterization of examples quadratic curvature decay, preprint, http://www.ugr.es/local/jperez/papers/papers.htm.
  • W. H. Meeks III and H. Rosenberg, The minimal lamination closure theorem, Duke Math. J. 133 (2006), 467--497.
  • A. V. Pogorelov, On the stability of minimal surfaces, Dokl. Akad. Nauk SSSR 260 (1981), 293--295.
  • A. Ros, One-sided complete stable minimal surfaces, J. Differential Geom. 74 (2006), 69--92.
  • R. Schoen, Estimates for stable minimal surfaces in three dimensional manifolds, Ann. of Math. Stud., 103, pp. 111--126, Princeton Univ. Press, Princeton, NJ, 1983.