## Solution of the Plateau problem for $$m$$-dimensional surfaces of varying topological type.(English)Zbl 0099.08503

### Keywords:

variational calculus
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 [1] A. S. Besicovitch, On the fundamental geometrical properties of linearly measurable plane sets of points II.Math. Ann., 115 (1938), 295–329. · Zbl 0018.11302 [2] –, A general form of the covering principle and relative differentiation of additive functions.Proc. Cambridge Phil. Soc., 41 (1945), 103–110. · Zbl 0063.00352 [3] –, Parametric Surfaces I. Compactness.Proc. Cambridge Phil. Soc., 45 (1949), 1–13. · Zbl 0037.04201 [4] –, Parametric Surfaces II. Lower Semi-continuity of the Area.Proc. Cambridge Phil. Soc., 45 (1949), 14–23. · Zbl 0037.04202 [5] J. Douglas, Minimal Surfaces of Higher Topological Structure.Ann. Math., 40 (1939), 205–298. [This paper contains many illustrations and also an extensive bibliography-including most of the author’s other papers in this field.] · Zbl 0020.37402 [6] S. Eilenberg & N. E. Steenrod,Foundations of Algebraic Topology. Princeton Mathematical Series No. 15. · Zbl 0047.41402 [7] F. Hausdorff,Mengenlehre. 3rd Edition. Dover Publications. [8] W. Hurewicz & H. Wallman,Dimension Theory. Princeton Mathematical Series No. 4. · Zbl 0036.12501 [9] E. R. Reifenberg, Parametric Surfaces I. Area.Proc. Cambridge Phil. Soc., 47 (1951), 687–698. · Zbl 0044.28002 [10] –, Parametric Surfaces V. Area II.Proc. Lond. Math. Soc., 19 (1955), 342–357. · Zbl 0066.04401 [11] –, Parametric Surfaces II. Tangential Properties.Proc. Cambridge Phil. Soc., 48 (1952), 46–69. · Zbl 0046.28302 [12] E. J. McShane, Parametrizations of Saddle Surfaces with Applications to the Problem of Plateau.Trans. Amer. Math. Soc., 35 (1933), 716–733. · Zbl 0007.11902
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