Literatur
Courant, R.: The existence of minimal surfaces of given topological structure under prescribed boundary conditions. Acta Math.72, 51–98 (1940).
—: On Plateau's problem with free boundaries. Proc. Nat. Acad. Sci. U.S.A.31, 242–246 (1945).
—: Dirichlet's principle, conformal mapping, and minimal surfaces. New York: Interscience Publ. 1950.
— Davids, N.: Minimal surfaces spanning closed manifolds. Proc. Nat. Acad. Sci. U.S.A.26, 194–199 (1940).
Davids, N.: Minimal surfaces spanning closed manifolds and having prescribed topological position. Amer. J. Math.64, 348–362 (1942).
Goldhorn, K.H.: Dissertation. Mainz 1971.
Harth, F.P.: Minimalflächen in Riemannschen Mannigfaltigkeiten mit freiem Rand. Dissertation. Mainz 1970.
Hildebrandt, S.: Über Minimalflächen mit freiem Rand. Math. Z.95, 1–19 (1967).
—: Boundary behavior of minimal surfaces. Arch. Rat. Mech. Analysis35, 47–82 (1969).
—: Über Flächen konstanter mittlerer Krümmung. Math. Z.112, 107–144 (1969).
Hildebrandt, S.: Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie. II. Freie Ränder. Arch. Rat. Mech. Analysis. Erscheint demnächst.
Hildebrandt, S., Jäger, W.: On the regularity of surfaces with prescribed mean curvature at a free boundary. Math. Z. Erscheint demnächst.
Jäger, W.: The behavior of minimal surfaces with free boundaries. Commun. Pure Appl. Math. Erscheint demnächst.
Lewy, H.: On minimal surfaces with partially free boundary. Commun. Pure Appl. Math.4, 1–13 (1951).
Morrey, C. B.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Soc.43, 126–166 (1938).
—: Multiple integral problems in the calculus of variations and related topics. Univ. California Publ. Math., New Ser.1, 1–130 (1943).
—: The problem of Plateau on a Riemannian manifold. Ann. of Math.49, 807–851 (1948).
—: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1966.
Nitsche, J. C. C.: The behavior of minimal surfaces with free boundaries. Remark on a paper by W. Jäger. Manuskript.
Warschawski, S.: On the differentiability at the boundary in conformal mapping. Proc. Amer. Math. Soc.12, 614–620 (1961).
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Goldhorn, K., Hildebrandt, S. Zum Randverhalten der Lösungen gewisser zweidimensionaler Variationsprobleme mit freien Randbedingungen. Math Z 118, 241–253 (1970). https://doi.org/10.1007/BF01109861
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DOI: https://doi.org/10.1007/BF01109861