References
[All 1] Allard, W.K.: On the first variation of a varifold. Ann. Math.95, 417–491 (1972)
[All 2] Allard, W.K.: On the first variation of a varifold: boundary behaviour. Ann. Math.101, 418–446 (1975)
[Alm 1] Almgren, F.J.: Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints. Mem. Am. Math. Soc.165 (1976)
[Alm 2] Almgren, F.J.: Optimal Isoperimetric Inequalities: Indiana Univ. Math. J.35, 451–547 (1986)
[BC] Brezis, H., Coron, J.-M.: Multiple solutions of H-systems and Rellich's conjecture. Commun. Pure Appl. Math.37, 149–187 (1984)
[DF 1] Duzaar, F., Fuchs, M.: On integral currents with constant mean curvature. Rend. Semin. Mat. Univ. Padova85, 79–103 (1991)
[DF2] Duzaar, F., Fuchs, M.: A general existence theorem for integral currents with prescribed mean curvature form. Boll. Unione Mat. Ital. (to appear)
[DF 3] Duzaar, F., Fuchs, M.: On the existence of integral currents with prescribed mean curvature vector. Manuscr. Math.67, 41–67 (1990)
[DS] Duzaar, F., Steffen, K.: A partial regularity theorem for harmonic maps at a free boundary. Asymptotic Anal.2, 299–343 (1989)
[Fe] Federer, H.: Geometric measure theory. Berlin Heidelberg New York: Springer 1969
[Fe 1] Federer, H.: The singular set of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension. Bull. Am. Math. Soc.76, 767–771 (1979)
[He] Heinz, E.: On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary. Arch. Ration. Mech. Anal.35, 249–252 (1969)
[HS] Hardt, R., Simon, L.: Boundary regularity and embedded solutions for the oriented Plateau problem. Ann. Math.110, 439–486 (1979)
[Gi] Giusti, E.: Minmal surfaces and functions of bounded variation. (Monogr. Math., Basel) Basel Boston Stuttgart: Birkhäuser 1984
[GG] Gonzalez, E.H.A., Greco, G.H.: Una nuova dimonstrazione della proprietà isoperimetrica dell'ipersfera nella classe degli insiemi aventi perimetro finito. Ann. Univ. Ferrara23, 251–256 (1977)
[GMT] Gonzalez, E., Massari, U., Tamanini, I.: On the regularity of boundaries of sets minimizing perimeter with a volume constraint. Indiana Univ. Math. J.32, 25–37 (1983)
[GT] Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order, second edition. Berlin Heidelberg New York: Springer 1977
[Gu] Gulliver, R.: On the nonexistence of a hypersurface of prescribed mean curvature with given boundary. Manuscr. Math.11, 15–39 (1974)
[MM] Massari, U., Miranda, M.: Minimal surfaces of codimension one. (Math. Stud., vol. 91) Amsterdam: North Holland 1984
[Mo] Morrey, C.B.: Second order elliptic systems of differential equations (Ann. Math. Stud., vol. 33, pp. 101–159) Princeton: Princeton University Press 1954
[Si] Simon, L.: Lectures on geometric measure theory: Canberra: Aust. Natl. Univ. 1984 (Proc. Cent. Math. Anal. Aust. Natl. Univ., vol. 3)
[Ste 1] Steffen, K.: Flächen vorgeschriebener mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt. Arch. Ration. Mech. Anal.49, 191–217 (1972)
[Ste 2] Steffen, K.: On the nonuniqueness of surfaces with prescribed mean curvature spanning a given contour. Arch. Ration. Mech. Anal.94, 101–122 (1986)
[Str 1] Struwe, M.: Nonuniqueness in the Plateau-problem for surfaces of constant mean curvature. Arch. Ration. Mech. Anal.93, 135–157 (1986)
[Str 2] Struwe, M.: Large H-surfaces via the mountain-pass-lemma. Math. Ann.270, 441–459 (1985)
[We 1] Wente, H.: A general existence theorem for surfaces of constant mean curvature. Math. Z.120, 277–288 (1971)
[We 2] Wente, H.: The Dirichlet problem with a volume constraint. Manuscr. Mat.11, 141–157 (1974)
[We 3] Wente, H.: Large solutions to the volume constrained Plateau problem. Arch. Ration. Mech. Anal.75, 59–77 (1980)
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Duzaar, F., Steffen, K. Area minimizing hypersurfaces with prescribed volume and boundary. Math Z 209, 581–618 (1992). https://doi.org/10.1007/BF02570855
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DOI: https://doi.org/10.1007/BF02570855