This is a preview of subscription content, log in via an institution to check access.
Literatur
Courant, R., Dirichlet's principle, conformal mapping and minimal surfaces. New York: Interscience 1950.
Eisenhart, L. P., An introduction to differential geometry. Princeton, N. J.: Princeton University Press 1947.
Gulliver II, R. D., The Plateau problem for surfaces of prescribed mean curvature in a riemannian manifold. J. Differential Geometry 8, 317–330 (1973).
Heinz, E., On certain nonlinear elliptic differential equations and univalent mappings. J. Analyse Mathematique 5, 197–272 (1956/57).
Heinz, E., Ein Regularitätssatz für Flächen beschränkter mittlerer Krümmung. Nachr. Akad. Wiss. Gött., II Math. Phys. Kl. Nr. 12 (1969).
Heinz, E., On surfaces of constant mean curvature with polygonal boundaries. Arch. Rational Mech. Anal. 36, 335–347 (1970).
Heinz, E., Unstable surfaces of constant mean curvature. Arch. Rational Mech. Anal. 38, 257–267 (1970).
Hildebrandt, S., Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie. Math. Z. 112, 205–213 (1969).
Hirsch, M. W., Differential topology. Berlin-Heidelberg-New York: Springer, 1976.
Jäger, W., Remarks on results of Heinz concerning the continuity of total variations. Arch. Rational Mech. Anal. 37, 21–28 (1970).
Jäger, W., Ein Maximumprinzip für ein System nichtlinearer Differentialgleichungen. Nachr. Akad. Wiss. Gött., Math. Phys. Kl., Nr. 11 (1976).
Jäger, W., & H. Kaul, Uniqueness and stability of harmonic maps and their Jacobi fields. Manuscripta Mathematica 28, 269–291 (1979).
Morrey, C. B., Multiple integrals in the calculus of variations. Berlin-HeidelbergNew York: Springer 1966.
Morse, M., & C. B. Tompkins, The existence of minimal surfaces of general critical types. Ann. of Math. 40, 443–472 (1939); 42, 331 (1941).
Morse, M., & C. B. Tompkins, Minimal surfaces of non-minimum type by a new mode of approximation. Ann. of Math. 42, 62–72 (1941).
Morse, M., & C. B. Tompkins, Unstable minimal surfaces of higher topological structure. Duke Mathematical J. 8, 350–375 (1941).
Nitsche, J. C. C., Vorlesungen über Minimalflächen. Berlin-Heidelberg-New York: Springer 1975.
Palais, R. S., & S. Smale, A generalized Morse theory. Bull. Amer. Math. Soc. 70, 165–172 (1964).
Shiffman, M., The Plateau problem for nonrelative minima. Ann. of Math. (2) 40, 834–854 (1939).
Shiffman, M., Unstable minimal surfaces with several bondaries. Ann. of Math. (2) 43, 197–222 (1942).
Shiffman, M., Unstable minimal surfaces with any rectifiable boundary. Proc. Nat. Acad. Sci. USA 28, 103–108 (1942).
Shiffman, M., Instability for double integral problems in the calculus of variations. Ann. of Math. 45, 543–576 (1944).
Ströhmer, G., Instabile Minimalflächen in Riemannschen Mannigfaltigkeiten nicht-positiver Schnittkrümmung. J. reine u. angew. Math. 315, 16–39 (1980).
Ströhmer, G., Instabile Flächen vorgeschriebener mittlerer Krümmung. Math. Z. 174, 119–133 (1980).
Tomi, F., Ein einfacher Beweis eines Regularitätssatzes für schwache Lösungen gewisser elliptischer Systeme. Math. Z. 112, 214–218 (1969).
Author information
Authors and Affiliations
Additional information
Vorgelegt von J. C. C. Nitsche
Rights and permissions
About this article
Cite this article
Ströhmer, G. Instabile Lösungen der Eulerschen Gleichungen gewisser variationsprobleme. Arch. Rational Mech. Anal. 79, 219–239 (1982). https://doi.org/10.1007/BF00251904
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00251904