A sufficiency theorem for the Plateau problem

Author:
J. W. Lawson

Journal:
Trans. Amer. Math. Soc. **64** (1948), 192-204

MSC:
Primary 49.0X

DOI:
https://doi.org/10.1090/S0002-9947-1948-0026258-2

MathSciNet review:
0026258

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References | Similar Articles | Additional Information

**[I]**L. Bianchi,*Vorlesungen über differentialgeometrie*, Leipzig, Teubner, 1899; 2d ed., 1910, p. 422.**[II]**G. A. Bliss,*Calculus of variations*, Carus Mathematical Monographs, 1925.**[III]**-,*Calculus of variations. Multiple integrals*, Mimeographed notes, University of Chicago, 1939.**[IV]**A. B. Carson,*An analogue of Green's theorem for multiple integral problems in the calculus of variations*, Thesis, Contributions to the Calculus of Variations, 1938-1941, The University of Chicago Press.**[V]**A. R. Forsyth,*The range of minimal surfaces providing a minimum area*, Annali di Matematica (3) vol. 21 (1913) pp. 121-142.**[VI]**A. W. Landers, Jr.,*Invariant multiple integrals in the calculus of variations*, Thesis, Contributions to the Calculus of Variations, 1938-1941, The University of Chicago Press.**[VII]**J. W. Lawson,*Minima of integrals over hypersurfaces,*Thesis, Contributions to the Calculus of Variations, 1942-1946, The University of Chicago Press.**[VIII]**A. W. Raab,*Jacobi's condition for multiple integral problems of the calculus of variations*, Thesis, Contributions to the Calculus of Variations, 1931-1932, The University of Chicago Press.**[IX]**T. Radó,*The Plateau problem*, Ergebnisse der Mathematik, vol. 2, Berlin, Springer, 1933, pp. 81-190.**[X]**William T. Reid,*The Jacobi condition for the double integral problem of the calculus of variations*, Duke Math. J.**5**(1939), 856–870. MR**0000466****[XI]**H. A. Schwarz,*Gesammelte mathemalische Abhandlungen*, vol. 1, Berlin, Springer, 1890, pp. 223-269.

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DOI:
https://doi.org/10.1090/S0002-9947-1948-0026258-2

Article copyright:
© Copyright 1948
American Mathematical Society