References
W.K. Allard, On the first variation of a varifold. Ann. of Math.95 (1972), 417–491
W.K. Allard, On the first variation of a varifold: boundary behaviour. Ann. of Math.101 (1975), 418–446
F.J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and sin-gularity structure. Mere. Amer. Math. Soc.165 (1976)
F.J. Almgren, Optimal Isoperimetric Inequalities. Indiana Univ. Math. J.35 (1986), 451–547
J. Brothers, Existence and structure of tangent cones at the boundary of an area minimizing integral current. Indiana Univ. Math. J.26 (1977), 1027–1044
E. Bombieri, E. De Giorgi, M. Miranda, Una maggiorazione a priori relative alle ipersuperficie minimali non-parametriche. Arch. Rat. Mech. Analysis 32 (1969), 255–267
F. Duzaar, On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions. Analyse non linéaire. Ann. Inst. H. Poincaré (1993)
F. Duzaar, Boundary regularity for area minimizing currents with prescribed vol-ume. Preprint no. 265, SFB 256 Bonn 1992
F. Duzaar, M. Fuchs, On the existence of integral currents with prescribed mean curvature vector. manus, math.67 (1990), 41–67
F. Duzaar, M. Fuchs, A general existence theorem for integral currents with pre-scribed mean curvature form. Bolletino U. M. I. (7) 6-B(1992), 901–912
E. De Giorgi, F. Colombini, L. C. Piccinini, Frontiere orientate di misura minima e questioni collegate. Scuola Norm. Sup. Pisa 1972
F. Duzaar, K. Steffen, Area minimizing hypersurfaces with prescribed volume and boundary. Math. Z.209 (1992), 581–618
F. Duzaar, If. Steffen, Comparison principles for hypersurfaces of prescribed mean curvature. Preprint 1993
F. Duzaar, K. Steffen, Boundary regularity for minimizing currents with pre scribed mean curvature. To appear in Calculus of Variations and PDE
Ecker, Area-minimizing integral currents with movable parts of prescribed mass. Analyse non linéaire. Ann. Inst. H. Poincaré 6 (1989), 261–293.
H. Federer, Geometric measure theory. Springer, Berlin-Heidelberg-New York 1969
H. Federer, The singular set of area minimizing rectifiable currents with codimen-sion one and of area minimizing flat chains modulo two with arbitrary codimension. Bull. Amer. Math. Soc.76 (1970), 767–771
E.H.A. Gonzalez, U. Massari, I. Tamanini, On the regularity of boundaries of sets minimizing perimeter with a volume constraint. Indiana Univ. Math.32 (1983), 25–37
D. Gilbarg, N.S. Trudinger, Elliptic partial differential equations of second order. Second edition, Springer, Berlin-Heidelberg-New York 1977
R. Hardt, L. Simon, Boundary regularity and embedded solutions for the oriented Plateau problem. Ann. of Math.110 (1979), 439–486
U. Massari, Esistenza e regolarità dele ipersuperfici di curvatura media assegnata in ℝn. Arch. Rat. Mech. Analysis55 (1974), 357–382
U. Massari, M. Miranda, Minimal surfaces of codimension one. Mathematics Stud-ies 91, North Holland 1984
R. Pilz, Thesis. Düsseldoff 1993
J.T. Pitts, Existence and regularity of minimal surfaces on Kiemannian manifolds. Mathematical notes, Princeton University Press, 1981
L. Simon, Lectures on geometric measure theory. Proceedings C. M. A. 3, Can-berra 1983
I. Tamanini, Regularity results for almost minimal oriented hypersuffaces. Quaderni del Departimento di Matematica del Univ. di Lecce Q1 1984
N. Trudinger, A new proof of the interior gradient bound for the minimal surface equation inn dimensions. Proc. Nat. Acad. Sci. U.S.A.69 (1972), 821–823
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Duzaar, F., Steffen, K. λ Minimizing currents. Manuscripta Math 80, 403–447 (1993). https://doi.org/10.1007/BF03026561
Issue Date:
DOI: https://doi.org/10.1007/BF03026561