Bibliography
Cesari, L., Surface Area. Princeton Univ. Press 1956.
Courant, R., Critical points and unstable minimal surfaces. Proc. Nat. Acad. Sci. U.S.A. 27, 51–57 (1941).
Courant, R., Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces. New York: Interscience 1950.
Douglas, J., Minimal surfaces of general topological structure with any finite number of assigned boundaries. J. Math. Phys. 15, 105–123 (1936).
Douglas, J., Minimal surfaces of higher topological structure. Ann. of Math. (2) 40, 205–298 (1939).
Fleming, W. H., An example in the problem of least area. Proc. Amer. Math. Soc. 7, 1063–1074 (1956).
Kruskal, M., The bridge theorem for minimal surfaces. Comm. P. Appl. Math. 7, 297–316 (1954).
Lévy, P., Le problème de Plateau. Mathematica 23, 1–45 (1947-48).
Lewy, H., On the boundary behavior of minimal surfaces. Proc. Nat. Acad. Sci. U.S.A. 37, 103–110 (1951).
Morozov, S. F., Generalization of a theorem of R. Courant. Izv. Vysš. Učebn. Zaved. Matematika No. 4 (17), 133–144 [Russian].
Morse, M., & C. Tompkins, The existence of minimal surfaces of general critical types. Ann. of Math. (2) 40, 443–472 (1939); (2) 42, 331 (1941).
Morse, M., & C. Tompkins, The continuity of the area of harmonic surfaces as a function of the boundary representation. Amer. J. Math. 63, 825–838 (1941).
Morse, M., & C. Tompkins, Minimal surfaces of non-minimum type by a new mode of approximation. Ann. of Math. (2) 42, 62–72 (1941).
Nitsche, J. C. C., On new results in the theory of minimal surfaces. Bull. Amer. Math. Soc. 71, 195–270 (1965).
Radó, T., The problem of the least area and the problem of Plateau. Math. Z. 32, 763–796 (1930).
Radó, T., Contributions to the theory of minimal surfaces. Acta Litt. Sci. Univ. Szeged 6, 1–20 (1932).
Schneider, R., A note on branch points of minimal surfaces. Proc. Amer. Math. Soc. 17, 1254–1257 (1966).
Shiffman, M., The Plateau problem for non-relative minima. Ann. of Math. (2) 40, 834–854 (1939).
Shiffman, M., Unstable minimal surfaces with any rectifiable boundary. Proc. Nat. Acad. Sci. U.S.A. 28, 103–108 (1942).
Author information
Authors and Affiliations
Additional information
The preceding research was sponsored by the Air Force Office of Scientific Research under AFOSR Grant No. 883-67.
The author thanks Professor J. Leavitt for his assistance in the computation of the numerical values r 0 and gd 0.
Rights and permissions
About this article
Cite this article
Nitsche, J.C.C. Contours bounding at least three solutions of Plateau's problem. Arch. Rational Mech. Anal. 30, 1–11 (1968). https://doi.org/10.1007/BF00253243
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00253243