On minimal surfaces with free boundaries in given homotopy classes

Peter Tolksdorf

Annales de l'I.H.P. Analyse non linéaire (1985)

  • Volume: 2, Issue: 3, page 157-165
  • ISSN: 0294-1449

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Tolksdorf, Peter. "On minimal surfaces with free boundaries in given homotopy classes." Annales de l'I.H.P. Analyse non linéaire 2.3 (1985): 157-165. <http://eudml.org/doc/78094>.

@article{Tolksdorf1985,
author = {Tolksdorf, Peter},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {minimal surfaces; free boundary problem; pinching condition; homotopy classes},
language = {eng},
number = {3},
pages = {157-165},
publisher = {Gauthier-Villars},
title = {On minimal surfaces with free boundaries in given homotopy classes},
url = {http://eudml.org/doc/78094},
volume = {2},
year = {1985},
}

TY - JOUR
AU - Tolksdorf, Peter
TI - On minimal surfaces with free boundaries in given homotopy classes
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1985
PB - Gauthier-Villars
VL - 2
IS - 3
SP - 157
EP - 165
LA - eng
KW - minimal surfaces; free boundary problem; pinching condition; homotopy classes
UR - http://eudml.org/doc/78094
ER -

References

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  1. [1] H.W. Alt, F. Tomi, Regularity and finiteness of solutions to the free boundary problem for minimal surfaces, preprint. Zbl0549.53006MR779219
  2. [2] R. Courant, Dirichlet's principle, conformal mappings, and minimal surfaces, reprint by Springer-Verlag, New York-Heidelberg-Berlin, 1977. Zbl0354.30012MR454858
  3. [3] M. Grüter, J. Jost, On embedded minimal surfaces in convex bodies, preprint. Zbl0617.49017
  4. [4] S. Hildebrant, Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie II. Freie Ränder. Arch. Rat. Mech. Anal., t. 39, 1970, p. 275-293. Zbl0225.49039MR273524
  5. [5] S. Hildebrandt, J.C.C. Nitsche, Minimal surfaces with free boundaries, Acta Math., t. 23, 1979, p. 803-818. Zbl0444.49035MR549778
  6. [6] S. Hildebrandt, J.C.C. Nitsche, Geometrical properties of minimal surfaces with free boundaries. Math. Z., t. 184, 1983, p. 497-509. Zbl0505.49020MR719490
  7. [7] A. Küster, An optimal estimate of the free boundary of a minimal surface. Journal f. d. reine angew. Math., t. 349, 1984, p. 55-62. Zbl0527.53006MR743964
  8. [8] H. Lewy, On minimal surfaces with partially free boundary. Comm. P. Appl. Math., t. 4, 1951, p. 1-13. MR52711
  9. [9] W.H. Meeks, S.T. Yau, Topology of three dimensional manifolds and the embedding problem in minimal surface theory. Ann. of Math., t. 112, 1980, p. 441-484. Zbl0458.57007MR595203
  10. [10] J.C.C. Nitsche, Vorlesungen über Minimalflächen, Springer-Verlag, Berlin-Heidelberg-New York, 1975. Zbl0319.53003MR448224
  11. [11] J.C.C. Nitsche, The regularity of the trace for minimal surfaces. Annali della S. N. S. di Pisa, t. 3, 1976, p. 139-155. Zbl0331.53006MR402624
  12. [12] J.C.C. Nitsche, Stationary partioning of convex bodies. Arch. Rat. Mech. Anal. (to appear). Zbl0572.52005MR784101
  13. [13] B. Smyth, Stationary minimal surfaces with boundary on a simplex, Invent. Math. (to appear). Zbl0527.53005MR746536
  14. [14] M. Struwe, On a free boundary problem for minimal surfaces. Invent. Math., t. 75, 1984, p. 547-560. Zbl0537.35037MR735340
  15. [15] F. Tomi, A finiteness result in the free boundary value problem for minimal surfaces, preprint. Zbl0603.49028
  16. [16] N. Dauids, Minimal surfaces spanning closed manifolds and having prescribed topological position. Amer. J. Math., t. 64, 1942, p. 348-362. Zbl0063.01046MR6031

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