On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions
Duzaar, Frank
Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993), p. 191-214 / Harvested from Numdam
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Publié le : 1993-01-01
@article{AIHPC_1993__10_2_191_0,
     author = {Duzaar, Frank},
     title = {On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {10},
     year = {1993},
     pages = {191-214},
     mrnumber = {1220033},
     zbl = {0808.49036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1993__10_2_191_0}
}

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, Tome 10 (1993) pp. 191-214. http://gdmltest.u-ga.fr/item/AIHPC_1993__10_2_191_0/

[AW] W.K. Allard, On the first variation of a varifold, Ann. of Math., Vol. 95, 1972, pp. 417-491. | MR 307015 | Zbl 0252.49028

[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. | MR 1155829 | Zbl 0754.53010

[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. | MR 1037996 | Zbl 0703.49035

[DF3] F. Duzaar and M. Fuchs, On integral currents with constant mean curvature, Rend. Sem. Mat. Univ. Padova, Vol. 85, 1991, pp. 79-103. | Numdam | MR 1142534 | Zbl 0739.49026

[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). | MR 1200740 | Zbl 0786.49025

[Fe] H. Federer, Geometric measure theory, Springer, Berlin, Heidelberg, New York, 1969. | MR 257325 | Zbl 0176.00801

[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. | MR 260981 | Zbl 0194.35803

[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. | MR 308904 | Zbl 0233.53004

[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. | MR 298515 | Zbl 0214.11103

[GT] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, second Ed., Springer, Berlin, Heidelberg, New York, 1977. | MR 473443 | Zbl 0361.35003

[Hi] S. Hildebrandt, Randwertprobleme für Flächen vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapilaritätstheorie. I. Math. Z., Vol. 115, 1969, pp. 169-178. | MR 266115 | Zbl 0185.50201

[Ma] U. Massari, Esistenza e Regolarità delle Ipersuperfici di Curvatura Media Assegnata in Rn, Arch. Rat. Mech. Anal., Vol. 55, 1974, pp. 357-382. | MR 355766 | Zbl 0305.49047

[Mo] C.B. Morrey, Second order elliptic systems of differential equations, Ann. of Math. Studies, No. 33, Princeton Univ. Press, 1954, pp. 101-159. | MR 68091 | Zbl 0057.08301

[Si] L. Simon, Lectures on geometric measure theory, Proceedings C.M.A. 3, Canberra, 1983. | MR 756417 | Zbl 0546.49019

[St1] K. Steffen, Isoperimetric inequalities and the problem of Plateau, Math. Ann., Vol. 222, 1976, pp. 97-144. | MR 417903 | Zbl 0345.49024

[St2] K. Steffen, On the existence of surfaces with prescribed mean curvature and boundary, Math. Z., Vol. 146, 1976, pp. 113-135. | MR 394394 | Zbl 0343.49016