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Reifenberg, E. R.

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

Acta Math. 104, 1-92 (1960).
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Cited in 10 Reviews
Cited in 221 Documents

Keywords:

variational calculus
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References:

[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 · doi:10.1017/S0305004100022453
[3] –, Parametric Surfaces I. Compactness.Proc. Cambridge Phil. Soc., 45 (1949), 1–13. · Zbl 0037.04201 · doi:10.1017/S0305004100000384
[4] –, Parametric Surfaces II. Lower Semi-continuity of the Area.Proc. Cambridge Phil. Soc., 45 (1949), 14–23. · Zbl 0037.04202 · doi:10.1017/S0305004100000402
[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 · doi:10.2307/1968552
[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 · doi:10.1017/S0305004100027146
[10] –, Parametric Surfaces V. Area II.Proc. Lond. Math. Soc., 19 (1955), 342–357. · Zbl 0066.04401 · doi:10.1112/plms/s3-5.3.342
[11] –, Parametric Surfaces II. Tangential Properties.Proc. Cambridge Phil. Soc., 48 (1952), 46–69. · Zbl 0046.28302 · doi:10.1017/S0305004100027365
[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 · doi:10.1090/S0002-9947-1933-1501713-3
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