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The equivariant Plateau problem and interior regularity. (English) Zbl 0279.49043

MSC:
49Q20 Variational problems in a geometric measure-theoretic setting
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
35D10 Regularity of generalized solutions of PDE (MSC2000)
28A75 Length, area, volume, other geometric measure theory
58A25 Currents in global analysis
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[1] W. Allard, Boundary regularity for the Plateau problem, Ph. D. Thesis, Brown University, Providence, Rhode Island, 1968.
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[3] E. Bombieri, E. De Giorgi, and E. Giusti, Minimal cones and the Bernstein problem, Invent. Math. 7 (1969), 243 – 268. · Zbl 0183.25901 · doi:10.1007/BF01404309 · doi.org
[4] John E. Brothers, Integral geometry in homogeneous spaces, Trans. Amer. Math. Soc. 124 (1966), 480 – 517. · Zbl 0166.18103
[5] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. · Zbl 0176.00801
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[7] Herbert Federer, The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension, Bull. Amer. Math. Soc. 76 (1970), 767 – 771. · Zbl 0194.35803
[8] Wu-yi Hsiang and H. Blaine Lawson Jr., Minimal submanifolds of low cohomogeneity, J. Differential Geometry 5 (1971), 1 – 38. · Zbl 0219.53045
[9] Barrett O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459 – 469. · Zbl 0145.18602
[10] E. R. Reifenberg, On the analyticity of minimal surfaces, Ann. of Math. (2) 80 (1964), 15 – 21. · Zbl 0151.16702 · doi:10.2307/1970489 · doi.org
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