On solutions of the exterior Dirichlet problem for the minimal surface equation

Ernst Kuwert

Annales de l'I.H.P. Analyse non linéaire (1993)

  • Volume: 10, Issue: 4, page 445-451
  • ISSN: 0294-1449

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Kuwert, Ernst. "On solutions of the exterior Dirichlet problem for the minimal surface equation." Annales de l'I.H.P. Analyse non linéaire 10.4 (1993): 445-451. <http://eudml.org/doc/78312>.

@article{Kuwert1993,
author = {Kuwert, Ernst},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {exterior domains; maximum principle at infinity},
language = {eng},
number = {4},
pages = {445-451},
publisher = {Gauthier-Villars},
title = {On solutions of the exterior Dirichlet problem for the minimal surface equation},
url = {http://eudml.org/doc/78312},
volume = {10},
year = {1993},
}

TY - JOUR
AU - Kuwert, Ernst
TI - On solutions of the exterior Dirichlet problem for the minimal surface equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1993
PB - Gauthier-Villars
VL - 10
IS - 4
SP - 445
EP - 451
LA - eng
KW - exterior domains; maximum principle at infinity
UR - http://eudml.org/doc/78312
ER -

References

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  1. [1] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser Verlag, Boston, Basel, Stuttgart, 1984. Zbl0545.49018MR775682
  2. [2] A. Haar, Über das Plateausche Problem, Math. Ann., Vol. 97, 1927, pp. 124-258. Zbl52.0710.02MR1512358JFM52.0710.02
  3. [3] H. Jenkins and J. Serrin, The Dirichlet Problem for the Minimal Surface Equation in Higher Dimension, J. Reine Ang. Math., Vol. 229, 1968, pp. 170-187. Zbl0159.40204MR222467
  4. [4] N. Korevaar, R. Kusner and B. Solomon, The Structure of Complete Embedded Surfaces with Constant Mean Curvature, J. Differential Geometry, Vol. 30, 1989, pp. 465-503. Zbl0726.53007MR1010168
  5. [5] R. Krust, Remarques sur le problème extérieur de Plateau, Duke Math. J., Vol. 59, 1989, pp. 161-173. Zbl0709.49022MR1016882
  6. [6] E. Kuwert, Embedded Solutions for Exterior Minimal Surface Problems, Manuscripta math., Vol. 70, 1990, pp. 51-65. Zbl0717.49034MR1080902
  7. [7] R. Langévin and H. Rosenberg, A Maximum Principle at Infinity for Minimal Surfaces and Applications, Duke Math. J., Vol. 57, 1988, pp. 819-828. Zbl0667.49024MR975123
  8. [8] W.H. Meeks and H. Rosenberg, The Maximum Principle at Infinity for Minimal Surfaces in Flat Three Manifolds, Amhrest preprint, 1988. 
  9. [9] W.H. Meeks and S.T. Yau, The Existence of Embedded Minimal Surfaces and the Problem of Uniqueness, Math. Z., Vol. 179, 1982, pp. 151-168. Zbl0479.49026MR645492
  10. [10] J. Moser, On Harnack's Theorem for Elliptic Differential Equations, Comm. Pure Appl. Math., Vol. 14, 1961, pp. 577-591. Zbl0111.09302MR159138
  11. [11] R. Osserman, A Survey of Minimal Surfaces, Dover publ.2nd ed., New York, 1986. MR852409
  12. [12] R. Schoen, Uniqueness, Symmetry and Embeddedness of Minimal Surfaces, J. Differential Geometry, Vol. 18, 1983, pp. 791-809. Zbl0575.53037MR730928
  13. [13] F. Tomi and R. Ye, The Exterior Plateau Problem, Math. Z., Vol. 205, 1990, pp. 223-245. Zbl0719.53006MR1076131

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