On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions

Frank Duzaar

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

  • Volume: 10, Issue: 2, page 191-214
  • ISSN: 0294-1449

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Duzaar, Frank. "On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions." Annales de l'I.H.P. Analyse non linéaire 10.2 (1993): 191-214. <http://eudml.org/doc/78300>.

@article{Duzaar1993,
author = {Duzaar, Frank},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {surfaces of prescribed mean curvature; Plateau's problem; admissible currents},
language = {eng},
number = {2},
pages = {191-214},
publisher = {Gauthier-Villars},
title = {On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions},
url = {http://eudml.org/doc/78300},
volume = {10},
year = {1993},
}

TY - JOUR
AU - Duzaar, Frank
TI - On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1993
PB - Gauthier-Villars
VL - 10
IS - 2
SP - 191
EP - 214
LA - eng
KW - surfaces of prescribed mean curvature; Plateau's problem; admissible currents
UR - http://eudml.org/doc/78300
ER -

References

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  2. [DF1] F. Duzaar and M. Fuchs, Einige Bemerkungen über die Existenz orientierter Mannigfaltigkeiten mit vorgeschriebener mittlerer Krümmung, Zeitschrift für Analysis und ihre Anwendungen, Vol. 10, 4, 1991, pp. 525-534. Zbl0754.53010MR1155829
  3. [DF2 F. Duzaar and M. Fuchs, On the existence of integral currents with prescribed mean curvature vector, Manus. math., Vol. 67, 1990, pp. 41-67. Zbl0703.49035MR1037996
  4. [DF3] F. Duzaar and M. Fuchs, On integral currents with constant mean curvature, Rend. Sem. Mat. Univ. Padova, Vol. 85, 1991, pp. 79-103. Zbl0739.49026MR1142534
  5. [DF4] F. Duzaar and M. Fuchs, A general existence theorem for integral currents with prescribed mean curvature form, in Boll. U.M.I., 1992 (to appear). Zbl0786.49025MR1200740
  6. [Fe] H. Federer, Geometric measure theory, Springer, Berlin, Heidelberg, New York, 1969. Zbl0176.00801MR257325
  7. [Fe1] H. Federger, The singular set of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension, Bull. Amer. Math. Soc., Vol. 76, 1970, pp. 767-771. Zbl0194.35803MR260981
  8. [GS1] R. Gulliver and J. Spruck, Existence theorems for parametric surfaces of prescribed mean curvature, Indiana Univ. Math. J., Vol. 22, 1972, pp. 258-287. Zbl0233.53004MR308904
  9. [GS2] R. Gulliver and J. Spruck, The Plateau problem for surfaces of prescribed mean curvature in a cylinder, Invent. Math., Vol. 13, 1971, pp. 169-178. Zbl0214.11103MR298515
  10. [GT] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, second Ed., Springer, Berlin, Heidelberg, New York, 1977. Zbl0361.35003MR473443
  11. [Hi] S. Hildebrandt, Randwertprobleme für Flächen vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapilaritätstheorie. I. Math. Z., Vol. 115, 1969, pp. 169-178. Zbl0185.50201MR266115
  12. [Ma] U. Massari, Esistenza e Regolarità delle Ipersuperfici di Curvatura Media Assegnata in Rn, Arch. Rat. Mech. Anal., Vol. 55, 1974, pp. 357-382. Zbl0305.49047MR355766
  13. [Mo] C.B. Morrey, Second order elliptic systems of differential equations, Ann. of Math. Studies, No. 33, Princeton Univ. Press, 1954, pp. 101-159. Zbl0057.08301MR68091
  14. [Si] L. Simon, Lectures on geometric measure theory, Proceedings C.M.A.3, Canberra, 1983. Zbl0546.49019MR756417
  15. [St1] K. Steffen, Isoperimetric inequalities and the problem of Plateau, Math. Ann., Vol. 222, 1976, pp. 97-144. Zbl0345.49024MR417903
  16. [St2] K. Steffen, On the existence of surfaces with prescribed mean curvature and boundary, Math. Z., Vol. 146, 1976, pp. 113-135. Zbl0343.49016MR394394

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