This is a preview of subscription content, log in via an institution to check access.
References
Barbosa, J., do Carmo, M.: Stable minimal surfaces. Bull. Amer. Math. Soc.80, 581–583 (1974)
Beeson, M.: On interior branch points of minimal surfaces. Math. Z.171, 133–154 (1980)
Beeson, M., Tromba, A.J.: The cusp catastrophe of Thom in the bifurcation of minimal surfaces. Preprint
Böhme, R.: Die Zusammenhangskomponenten der Lösungen analytischer Plateauprobleme. Math. Z.133, 31–40 (1973)
Böhme, R., Tomi, F.: Zur Struktur der Lösungsmenge des Plateauproblems. Math. Z.133, 1–29 (1973)
Böhme, R., Tromba, A.J.: The index theorem for classical minimal surfaces. Preprint
Borevich, Z., Shafarevich, I.: Number Theory. New York-London: Academic Press 1966
Douglas, J.: Solution to the problem of Plateau. Trans. Amer. Math. Soc.33, 263–321 (1931)
Giesecke, B.: Simpliziale Zerlegung abzählbarer komplexer Räume. Thesis, A. Schubert, München (1963)
Gromoll, D., Meyer, W.: On differentiable functions with isolated critical points. Topology8, 361–369 (1969)
Gulliver, R., Lesley, D.: On boundary branch points of minimizing surfaces. Arch. Rational Mech. Anal.52, 20–25 (1973)
Gulliver, R., Osserman, R., Royden, H.: A theory of branched immersions of surfaces. Amer. J. Math.95, 750–812 (1973)
Hardt, R.: Stratification of real-analytic mappings and images. Invent. Math.28, 193–208 (1975)
Hellwig, G.: Partielle Differential-Gleichungen. Stuttgart: Teubner 1960
Hildebrandt, S.: Über das Randverhalten von Minimalflächen. Math. Ann.165, 1–18 (1966)
Hironaka, H.: Triangulation of algebraic sets. In: Proceedings of Symposia in Pure Mathematics 29 (Arcata 1974), pp. 165–185. Providence, Rhode Island: American Mathematical Society 1975
Kato, T.: Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York: Springer 1976
Lojasiewicz, S.: Triangulation of semi-analytic sets. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. (3)18, 449–474 (1964)
Morrey, C., Jr.: Multiple Integrals in the Calculus of Variations. Berlin-Heidelberg-New York: Springer 1966
Nitsche, J.C.C.: Vorlesungen über Minimalflächen. Berlin-Heidelberg-New York: Springer 1975
Osserman, R.: A Survey of Minimal Surfaces. New York-Toronto-London: Van Nostrand 1969
Osserman, R.: A proof of the regularity everywhere of the classical solution of Plateau's problem. Ann. Math.91, 550–569 (1970)
Protter, M., Weinburger, H.: Maximum Principles in Differential Equations. Englewood Cliffs, New Jersey: Prentice-Hall 1967
Sato, K.: Local triangulations of real-analytic varieties. Osaka Z. Math.15, 109–125 (1963)
Schüffler, K.: Die Variation des konformen Typs mehrfach zusammenhängender Minimalflächen; Anwendung auf die Isoliertheit und Stabilität des Plateau-problems. Thesis, Saarbrücken (1978)
Tomi, F.: On the local uniqueness of the problem of least area. Arch. Rational Mech. Anal.52, 312–318 (1973)
Tomi, F.: On the finite solvability of Plateau's problem. In: Geometry and Topology. III Latin American School of Mathematics (Rio de Janeiro, 1976), pp. 679–695. Lecture Notes in Mathematics597, Berlin-Heidelberg-New York: Springer 1977
Tromba, A.J.: On the number of simply connected minimal surfaces spanning a curve. Mem. Amer. Math. Soc. 12, No. 194 (1977)
Tromba, A.J.: On the local bilinearization of the Dirichlet functional about a non-degenerate minimal surface. Preprint
Author information
Authors and Affiliations
Additional information
It is a pleasure to thank S. Hildebrandt and SFB 72 for support during the preparation of this paper
Rights and permissions
About this article
Cite this article
Beeson, M. Some results on finiteness in Plateau's problem, part I. Math Z 175, 103–123 (1980). https://doi.org/10.1007/BF01674441
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01674441