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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Existence and regularity of minimal surfaces on Riemannian manifolds


Author: Jon T. Pitts
Journal: Bull. Amer. Math. Soc. 82 (1976), 503-504
MSC (1970): Primary 49F10, 49F20, 49F22
MathSciNet review: 0405219
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References [Enhancements On Off] (What's this?)

  • [AF] F. J. Almgren, Jr., The theory of varifolds. Mimeographed notes, Princeton (1965)
  • Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325 (41 #1976)
  • H. Blaine Lawson Jr., The global behavior of minimal surfaces in 𝑆ⁿ, Ann. of Math. (2) 92 (1970), 224–237. MR 0270279 (42 #5169)
  • Marston Morse and C. Tompkins, The existence of minimal surfaces of general critical types, Ann. of Math. (2) 40 (1939), no. 2, 443–472. MR 1503471, http://dx.doi.org/10.2307/1968932
  • [PJ1] J. Pitts, Existence of minimal surfaces on riemannian manifolds I: Almost minimizing varifolds (preprint).
  • [PJ2] J. Pitts, Existence of minimal surfaces on riemannian manifolds II: Regular surfaces in three dimensional manifolds (preprint).
  • Max Shiffman, The Plateau problem for non-relative minima, Ann. of Math. (2) 40 (1939), 834–854. MR 0000467 (1,79a)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1976-14075-X
PII: S 0002-9904(1976)14075-X