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On Plateau's problem for minimal surfaces of higher genus in ${\mathbf{R}}^3 $
Author(s):
Friedrich
Tomi;
Anthony
Tromba
Journal:
Bull. Amer. Math. Soc.
13
(1985),
169-171.
MSC (1980):
Primary 53A10, 49F10
MathSciNet review:
799805
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Additional information
References:
- 1.
- Richard Courant, The existence of minimal surfaces of given topological type, Acta Math. 72 (1940), 51-98. MR 2478
- 2.
- Richard Courant and Herbert Robbins, What is mathematics?, Oxford Univ. Press, New York, 1941. MR 5358
- 3.
- Jesse Douglas, Solution to the problem of Plateau, Trans. Amer. Math. Soc. 33 (1931), 263-321. MR 1501590
- 4.
- Jesse Douglas, Minimal surfaces of higher topological structure, Ann. of Math. (2) 40 (1939), 205-298. MR 1503457
- 5.
- R. Gulliver, R. Ossermer and H. L. Royden, A theory of branched immersions, Amer. J. Math. 95 (1973), 750-811. MR 362153
- 6.
- R. Gulliver, Branched immersions of surfaces and reduction of topological type. II, Math. Ann. 230 (1977), 23-48. MR 464078
- 7.
- Bob Hardt and Leon Simon, Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math. (2) 110 (1979), 439-486. MR 554379
- 8.
- Stefan Hildebrandt, Boundary behavior of minimal surfaces, Arch. Rational Mech. Anal. 35 (1969), 47-81. MR 248650
- 9.
- J. Nielsen, Die Isomorphismen der allgemeinen unendlichen Gruppe mit zwei Erzeugenden, Math. Ann. 78 (1918), 385-397. MR 1511907
- 10.
- Tibor Radó, On the Problem of Plateau, Ergeb. Math. Grenzgeb., Springer-Verlag, (1933).
- 11.
- Rick Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of three manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), 127-142. MR 541332
- 12.
- Friedrich Tomi, Variationsprobleme vom Dirichlet-Typ mit einer Ungleichung als Nebenbedingung, Math. Z. 128 (1972), 43-74. MR 322624
- 13.
- Heiner Zieschang, Alternierende Produkte in freien Gruppen, Abh. Math. Sem. Univ. Hamburg 27 (1964), 12-31. MR 161901
- 14.
- Luc Lemaire, Boundary value problems for harmonic and minimal maps of surfaces into manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 9 (1982), 91-103. MR 664104
- 15.
- William H. Meeks, Uniqueness theorems for minimal surfaces, Illinois J. Math. 25 (1981), 318-336. MR 607034
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Additional Information:
DOI:
10.1090/S0273-0979-1985-15409-6
PII:
S 0273-0979(1985)15409-6
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