×

zbMATH — the first resource for mathematics

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

PDF BibTeX XML Cite
Full Text: DOI
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.