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Geometric properties of minimal surfaces with free boundaries. (English) Zbl 0505.49020


MSC:

49Q05 Minimal surfaces and optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
28A75 Length, area, volume, other geometric measure theory
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References:

[1] Allard, W.K.: On the first variation of a varifold. Ann. of Math. (2)95, 417-491 (1972) · Zbl 0252.49028
[2] Dziuk, G.: On the boundary behaviour of partially free minimal surfaces. Manuscripta Math.53, 105-123 (1981) · Zbl 0477.49024
[3] Dziuk, G.: Über die Stetigkeit teilweise freier Minimalflächen. Manuscripta Math.36, 241-251 (1981) · Zbl 0468.49023
[4] Goldhorn, K.H., Hildebrandt, S.: Zum Randverhalten der Lösungen gewisser zweidimensionaler Variationsprobleme mit freien Randbedingungen. Math. Z.118, 241-253 (1970) · Zbl 0202.20502
[5] Grüter, M., Hildebrandt, S., Nitsche, J.C.C.: On the boundary behavior of minimal surfaces with a free boundary which are not minima of the area. Manuscripta Math.35, 387-410 (1981) · Zbl 0483.49037
[6] Gulliver, R.D., Lesley, F.D.: On boundary branch points of minimizing surfaces. Arch. Rational Mech. Anal.52, 20-25 (1973) · Zbl 0263.53009
[7] Gulliver, R.D., Osserman, R., Royden, H.L.: A theory of branched immersions of surfaces. Amer. J. Math.95, 750-812 (1973) · Zbl 0295.53002
[8] Hildebrandt, S.: Ein einfacher Beweis für die Regularität der Lösungen gewisser zweidimensionaler Variationsprobleme unter freien Randbedingungen. Math. Ann.194, 316-331 (1971) · Zbl 0219.49015
[9] Hildebrandt, S.: Maximum principles for minimal surfaces and for surfaces of constant mean curvature. Math. Z.128, 253-269 (1972) · Zbl 0253.53005
[10] Hildebrandt, S., Nitsche, J.C.C.: Minimal surfaces with free boundaries, Acta Math.143, 251-272 (1979) · Zbl 0444.49035
[11] Hildebrandt, S., Nitsche, J.C.C.: Optimal boundary regularity for minimal surfaces with a free boundary. Manuscripta Math.33, 357-364 (1981) · Zbl 0465.49029
[12] Jäger, W.: Behavior of minimal surfaces with free foundaries. Comm. Pure Appl. Math.23, 803-818 (1970) · Zbl 0204.11601
[13] Lévy, P.: Surfaces minima et corps convexes moyenne. C.R. Acad. Sci. Paris Ser. A-B223, 881-883 (1946) · Zbl 0061.37703
[14] Lévy, P.: Le problème de Plateau. Mathematica (Cluj)23, 1-45 (1947-1948)
[15] Lewy, H.: On minimal surfaces with partially free boundary. Comm. Pure Appl. Math.4, 1-13 (1951) · Zbl 0042.15702
[16] McShane, E.J.: On the analytic nature of surfaces of least area. Ann. of Math. (2)35, 456-473 (1934) · Zbl 0010.06802
[17] Nitsche, J.C.C.: The boundary behavior of minimal surfaces. Kellogg’s theorem and branch points on the boundary. Invent. Math.8, 313-333 (1969) · Zbl 0195.23101
[18] Nitsche, J.C.C.: Minimal surfaces with partially free boundary. Least area property and Hölder continuity for boundaries satisfying a chord-arc condition. Arch. Rational Mech. Anal.39, 131-145 (1970) · Zbl 0209.41602
[19] Nitsche, J.C.C.: Vorlesungen über Minimalflächen. Berlin-Heidelberg-New York: Springer 1975 · Zbl 0319.53003
[20] Nitsche, J.C.C.: The regularity of the trace for minimal surfaces. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)3, 139-155 (1976) · Zbl 0331.53006
[21] Taylor, J.E.: Boundary regularity for various capillarity and boundary problems. Comm. Partial Differential Equations2, 323-357 (1977) · Zbl 0357.35010
[22] Wohlrab, O.: Einschließungssätze für Minimalflächen und Flächen mit vorgegebener mittlerer Krümmung. Bonner Math. Schriften138 (1982)
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