This is a preview of subscription content, log in via an institution to check access.
Bibliography
Courant, R., On a generalized form of Plateau's problem. Trans. Amer. Math. Soc. 50, 40–47 (1941).
Courant, R., On Plateau's problem with free boundaries. Proc. Nat. Acad. Sci. U. S. A. 31, 242–246 (1945).
Courant, R., Dirichlet's Principle, Conformal Mapping and Minimal Surfaces. New York: Interscience Publ. 1950.
Golusin, G. M., Geometrische Funktionentheorie. Berlin: Deutscher Verlag der Wissenschaften. 1957.
Heinz, E., Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung. Math. Ann. 127, 258–287 (1954).
Hildebrandt, S., Über das Randverhalten von Minimalflächen. Math. Ann. 165, 1–18 (1966).
Hildebrandt, S., Über Minimalflächen mit freiem Rand. Math. Z. 95, 1–19 (1967).
Hildebrandt, S., Über Flächen konstanter mittlerer Krümmung. To appear in Math. Z.
Hildebrandt, S., Einige Bemerkungen über Minimalflächen in Riemannschen Mannigfaltigkeiten. To appear.
Kellogg, O. D., Harmonic functions and Green's integrals. Trans. Amer. Math. Soc. 13, 109–132 (1912).
Kellogg, O. D., On the derivatives of harmonic functions on the boundary. Trans. Amer. Math. Soc. 33, 486–510 (1931).
Lewy, H., On the boundary behavior of minimal surfaces. Proc. Nat. Acad. Sci. U. S. A. 37, 103–110 (1951).
Lewy, H., On minimal surfaces with partially free boundary. Comm. Pure Appl. Math. 4, 1–13 (1951).
Morrey, C. B., On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc. 43, 126–166 (1938).
Morrey, C. B., The problem of Plateau on a Riemannian manifold. Ann. of Math. 49, 807–851 (1948).
Morrey, C. B., Multiple Integrals in the Calculus of Variations. Berlin-Heidelberg-New York: Springer 1966.
Nirenberg, L., Remarks on strongly elliptic partial differential equations. Comm. Pure Appl. Math. 8, 648–674 (1955).
Nirenberg, L., On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13, 115–162 (1959).
Nitsche, J. C. C., On new results in the theory of minimal surfaces. Bull. Amer. Math. Soc. 71, 195–270 (1965).
Painlevé, P., Comptes Rendus 112, 653–657 (1891).
Riesz, F. & M., Über die Randwerte einer analytischen Funktion. Quatrième congrès math. scand. 1916.
Riesz, F., Über die Randwerte einer analytischen Funktion. Math. Z. 18, 87–95 (1923).
Sasaki, S., On the total curvature of a closed curve. Japanese Journal Math. 29, 118–125 (1959).
Schneider, R., A note on branch points of minimal surfaces. Proc. Amer. Math Soc. 17, 1254–1257 (1966).
Seidel, W., Über die Ränderzuordnung bei konformen Abbildungen. Math. Ann. 104, 183–243 (1931).
Tsuji, M., On a theorem of F. and M. Riesz. Proc. Imp. Acad. Tokyo 18, 172–175 (1942).
Tsuji, M., Potential Theory in Modern Function Theory. Tokyo: Maruzen 1959.
Warschawski, S., Über das Randverhalten der Abbildungsfunktion bei konformer Abbildung. Math. Z. 35, 321–456 (1932).
Warschawski, S., On the higher derivatives at the boundary in conformal mapping. Trans. Amer. Math. Soc. 38, 310–340 (1935).
Warschawski, S., On the differentiability at the boundary in conformal mapping. Proc. Amer. Math. Soc. 12, 614–620 (1961).
Author information
Authors and Affiliations
Additional information
Communicated by J. C. C. Nitsche
Rights and permissions
About this article
Cite this article
Hildebrandt, S. Boundary behavior of minimal surfaces. Arch. Rational Mech. Anal. 35, 47–82 (1969). https://doi.org/10.1007/BF00248494
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00248494