The Euler characteristic of vector fields on Banach manifolds and the problem of Plateau

Antony Tromba

Mémoires de la Société Mathématique de France (1976)

  • Volume: 46, page 83-89
  • ISSN: 0249-633X

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Tromba, Antony. "The Euler characteristic of vector fields on Banach manifolds and the problem of Plateau." Mémoires de la Société Mathématique de France 46 (1976): 83-89. <http://eudml.org/doc/94731>.

@article{Tromba1976,
author = {Tromba, Antony},
journal = {Mémoires de la Société Mathématique de France},
language = {eng},
pages = {83-89},
publisher = {Société mathématique de France},
title = {The Euler characteristic of vector fields on Banach manifolds and the problem of Plateau},
url = {http://eudml.org/doc/94731},
volume = {46},
year = {1976},
}

TY - JOUR
AU - Tromba, Antony
TI - The Euler characteristic of vector fields on Banach manifolds and the problem of Plateau
JO - Mémoires de la Société Mathématique de France
PY - 1976
PB - Société mathématique de France
VL - 46
SP - 83
EP - 89
LA - eng
UR - http://eudml.org/doc/94731
ER -

References

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  1. [1] DOUGLAS J., Solution to the problem of Plateau, Trans. Amer. Math. Soc., 33, (1931), 263-321. Zbl0001.14102MR1501590JFM57.1542.03
  2. [2] COURANT R., Dirichlet's Principle, Interscience, New-York, 1950. Zbl0040.34603
  3. [3] ELIASSON H., Geometry of manifolds of maps, J. Diff. Geometry, 1 (1967), 169-194. Zbl0163.43901MR37 #2268
  4. [4] ELWORTHY K.K., and TROMBA A.J., Differentiable structures and Fredholm maps on Banach manifolds, Proc. Symp. on Global Analysis, Berkeley, 1968. Zbl0206.52504
  5. [5] HILDEBRANDT S., Boundary behavior of minimal surfaces, Arch. Rat. Mich. Anal. Zbl0183.39402
  6. [6] MORSE M., and TOMPKINS C., Existence of minimal surfaces of general critical type, Proc. Nat. Acad. Sciences U.S.A., 25 (1939), 153-158. Zbl0021.03404JFM65.0456.03
  7. [7] NITSCHE J.C.C., The boundary behavior of minimal surfaces, Kellog's theorem and branch points on the boundary, Inventiones Math., 8 (1969), 313-333. Zbl0195.23101MR41 #4399a
  8. [8] OSSERMAN R., A survey of Minimal Surfaces, Van Nostrand, Princeton, 1969. Zbl0209.52901MR41 #934
  9. [9] PALAIS R., Lectures on the Atiyah-Singer Index Theorem, Princeton, 1964. Zbl0202.23103
  10. [10] RADO T., On the problem of Plateau, Ergebnisse der Mathematik und Ihrer Grenzgebeite, Springer-Verlag, Berlin, 1933. Zbl0007.11804JFM59.1341.01
  11. [11] RADO T., The problem of least area and the problem of Plateau, Math. Z., 32 (1930), 763-796. Zbl56.0436.01JFM56.0436.01
  12. [12] SCHIFFMAN M., Plateau's problem for non-relative minima, Ann. Math., 40 (1939), 834-854. Zbl0023.39802MR1,79a
  13. [13] TROMBA A., Fredholm vector fields and a transversality theorem, preprint. Zbl0341.58005
  14. [14] TROMBA A., A generalized approach to Morse theory, to appear in J. Diff. Geometry. Zbl0344.58012
  15. [15] TROMBA A., The Morse-Sard-Brown theorem and the problem of Plateau, to appear in the Amer. J. Math. Zbl0373.58003
  16. [16] TROMBA A., On the number of simply connected minimal surfaces spanning a curve in R3, in preparation. Zbl0389.53003
  17. [17] TROMBA A., Théorie de Morse sur les variétés de Banach, C.R. Acad. Sc. Paris, (1975). Zbl0303.58006MR52 #15553

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