Curvature estimates for minimal surfaces in 3 -manifolds

Michael T. Anderson

Annales scientifiques de l'École Normale Supérieure (1985)

  • Volume: 18, Issue: 1, page 89-105
  • ISSN: 0012-9593

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Anderson, Michael T.. "Curvature estimates for minimal surfaces in $3$-manifolds." Annales scientifiques de l'École Normale Supérieure 18.1 (1985): 89-105. <http://eudml.org/doc/82157>.

@article{Anderson1985,
author = {Anderson, Michael T.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {interior curvature estimate; minimal embedded discs; 3-manifolds; stationary varifolds},
language = {eng},
number = {1},
pages = {89-105},
publisher = {Elsevier},
title = {Curvature estimates for minimal surfaces in $3$-manifolds},
url = {http://eudml.org/doc/82157},
volume = {18},
year = {1985},
}

TY - JOUR
AU - Anderson, Michael T.
TI - Curvature estimates for minimal surfaces in $3$-manifolds
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1985
PB - Elsevier
VL - 18
IS - 1
SP - 89
EP - 105
LA - eng
KW - interior curvature estimate; minimal embedded discs; 3-manifolds; stationary varifolds
UR - http://eudml.org/doc/82157
ER -

References

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  2. [Al2] W. K. ALLARD, On the first Variation of a Varifold : Boundary Behavior (Ann. of Math., vol. 101, 1975, pp. 418-446). Zbl0319.49026MR53 #1379
  3. [B] S. BERNSTEIN, Sur un théorème de géométrie et ses applications aux équations aux dérivées partielles du type elliptique (Comm. de la Soc. Math. de Karkov (2e série), Vol. 15, 1915, pp. 38-45). JFM48.1401.01
  4. [CS] H. I. CHOI and R. SCHOEN, The Space of Minimal Embeddings of a Surface Into a three Dimensional Manifold of Positive Ricci Curvature (to appear). Zbl0577.53044
  5. [GL] R. GULLIVER and F. D. LESLEY, On Boundary Branch Points of Minimizing Surfaces (Arch. Rat. Mech. Anal., Vol. 52, 1973, pp. 20-25). Zbl0263.53009MR49 #11366
  6. [JM] L. JORGE and W. MEEKS III, The Topology of Minimal Surfaces of Finite Total Gaussian Curvature, to appear in Topology. 
  7. [H] E. HEINZ, Über die Lösungen der Minimalflöchen gleichung (Nachr. Akad. Wiss. Göttingen Math. Phys., K1. II, 1952, pp. 51-56). Zbl0048.15401MR14,885c
  8. [L1] H. B. LAWSON, Jr., Complete Minimal Surfaces in S3 (Ann. of Math., Vol. 92, 1970, pp. 335-374). Zbl0205.52001MR42 #5170
  9. [L2] H. B. LAWSON, Jr., Minimal Varieties in Real and Complex Analysis, University of Montreal Press, 1974. 
  10. [N] J. C. C. NITSCHE, Contours Bounding at Most Finitely Many Solutions to Plateau's Problem (Complex Anal. and its Appl., Nauka, Moscow, 1978, pp. 438-446). Zbl0422.49031MR80e:53006
  11. [Ob] M. OBATA, Ed., Minimal Submanifolds and Geodesics, Kaigai Publ. Ltd. Tokyo, 1978. 
  12. [Os] R. OSSERMAN, On complete Minimal Surfaces (Arch. Rat. Mech. Anal., Vol. 13, 1963, pp. 392-404). Zbl0127.38003MR27 #1888
  13. [P] J. PITTS, Existence and Regularity of Minimal Surfaces on Riemannian Manifolds (Math. Notes 27, Princeton University Press, 1981). Zbl0462.58003MR83e:49079
  14. [S] R. SCHOEN, Estimates for Stable Minimal Surfaces in three Dimensional Manifolds (Annals of Math. Studies, Vol. 103, Princeton Univ. Press, 1983). Zbl0532.53042MR86j:53094
  15. [SS1] R. SCHOEN and L. SIMON, Regularity of Stable Minimal Hypersurfaces (Comm. Pure Appl. Math., Vol. 34, 1981, pp. 741-797). Zbl0497.49034MR82k:49054
  16. [SS2] R. SCHOEN and L. SIMON, Regularity of Simply Connected Surfaces with Quasiconformal Gauss Map (Annals of Math. Studies, Vol. 103, Princeton Univ. Press, 1983). Zbl0544.53001MR87b:53009
  17. [SSY] R. SCHOEN, L. SIMON and S.-T. YAU, Curvature Estimates for Minimal Hypersurfaces (Acta. Math., Vol. 134, 1975, pp. 276-288). Zbl0323.53039MR54 #11243
  18. [T] F. TOMI, On the Local Uniqueness of the Problem of Least area (Arch. Rat. Mech. Anal., Vol. 52, 1973, pp. 312-318). Zbl0277.49016MR49 #11364

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