Area-minimizing integral currents with movable boundary parts of prescribed mass
Annales de l'I.H.P. Analyse non linéaire, Volume 6 (1989) no. 4, p. 261-293 
@article{AIHPC_1989__6_4_261_0,
     author = {Ecker, Klaus},
     title = {Area-minimizing integral currents with movable boundary parts of prescribed mass},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {6},
     number = {4},
     year = {1989},
     pages = {261-293},
     zbl = {0677.49032},
     mrnumber = {998604},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1989__6_4_261_0}
}

Ecker, Klaus. Area-minimizing integral currents with movable boundary parts of prescribed mass. Annales de l'I.H.P. Analyse non linéaire, Volume 6 (1989) no. 4, pp. 261-293. http://www.numdam.org/item/AIHPC_1989__6_4_261_0/

[AA] W.K. Allard and F.J. Almgren, The Structure of Stationary One Dimensional Varifolds with Positive Density, Inv. math., Vol. 34, 1976, pp. 83-97. | MR 425741 | Zbl 0339.49020

[AW] W.K. Allard, On the First Variation of a Varifold, Annals of Math., Vol. 95, 1972, pp. 417-491. | MR 307015 | Zbl 0252.49028

[AHW] W.H. Alt, Die Existenz einer Minimalfläche mit freiem Rand vorgeschriebener Länge, Archive Rat. Mech. Analysis, Vol. 51, 1973, pp. 304-320. | MR 336528 | Zbl 0282.49039

[BJ] J. Brothers, Existence and Structure of Tangent Cones at the Boundary of an Area Minimizing Integral Current, Indiana Univ. Math., Vol. 26, 1977, pp. 1027- 1044. | MR 487727 | Zbl 0374.49022

[DHL] U. Dierkes, S. Hildebrandt and H. Lewy, On the Analyticity of Minimal Surfaces at Movable Boundaries of Prescribed Length, Journal f. d. Reine u. Angew. Mathematik, Vol. 379, 1987, pp. 100-114. | MR 903636 | Zbl 0617.53010

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

[HS] R. Hardt and L. Simon, Boundary Regularity and Embedded Solutions for the Oriented Plateau Problem, Annals of Math., Vol. 110, No. 1, 1979, pp. 439-486. | MR 554379 | Zbl 0457.49029

[HW] S. Hildebrandt and H.C. Wente, Variational Problems with Obstacles and a Volume Constraint; Math. Z., Vol. 135, 1973, pp. 55-68. | MR 365314 | Zbl 0284.49017

[N1] J.C.C. Nitsche, Vorlesungen über Minimalflächen, Springer, Berlin, Heidelberg, New York, 1975. | MR 448224 | Zbl 0319.53003

[N2] J.C.C. Nitsche, The Regularity of Minimal Surfaces on the Movable Parts of their Boundaries, Indiana Univ. Math. J., Vol. 21, 1971, pp. 505-513. | MR 290260 | Zbl 0236.53011

[N3] J.C.C. Nitsche, On the Boundary Regularity of Surfaces of Least Area in Euclidean Space, Continuum Mechanics and Related Problems of Analysis, Nauka, Moscow, 1972, pp. 375-377. | MR 394393 | Zbl 0254.53003

[SL] L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, Canberra, Vol. 3, 1983. | MR 756417 | Zbl 0546.49019

[WB] B. White, Regularity of Area-Minimizing Hypersurfaces at Boundaries with Multiplicites, in Seminar on minimal Submanifolds, E. BOMBIERI Ed., Annals of Math., Studies, Vol. 103, Princeton Univ. Press, 1983. | MR 795244 | Zbl 0528.53051