×

The isoperimetric inequality for doubly-connected minimal surfaces in \(\mathbb{R}^n\). (English) Zbl 0387.53002


MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
52A40 Inequalities and extremum problems involving convexity in convex geometry
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] E. F. Beckenbach,The area and boundary of minimal surfaces, Ann. of Math.33 (1932), 658–664. · Zbl 0005.26204
[2] T. Carleman,Zur Theorie der Minimalflächen, Math. Z.9 (1921), 154–160. · JFM 48.0590.02
[3] J. M. Feinberg,Some Wirtinger-like inequalities, to appear. · Zbl 0426.26008
[4] M. Morse and C. Tompkins,The continuity of the area of harmonic surfaces as a function of the boundary representation, Amer. J. Math.63 (1941), 825–838. · Zbl 0026.12404
[5] J. C. C. Nitsche,The isoperimetric inequality for multiply-connected surfaces, Math. Ann.160 (1965), 370–375. · Zbl 0144.20505
[6] J. C. C. Nitsche,Vorlesungen über Minimalflächen, Springer-Verlag, Berlin, 1975. · Zbl 0319.53003
[7] R. Osserman,A Survey of Minimal Surfaces, Van Nostrand-Reinhold, New York, 1969. · Zbl 0209.52901
[8] R. Osserman and M. Schiffer,Doubly-connected minimal surfaces, Arch. Rational Mech. Anal.58 (1975), 285–307. · Zbl 0352.53005
[9] G. Polya and G. Szegö,Aufgaben und Lehrsätze aus der Analysis, Erster Band, 4. Auflage, Springer-Verlag, Berlin, 1970.
[10] T. Rado,On the Problem of Plateau, Springer-Verlag, Berlin, 1933. · Zbl 0007.11804
[11] T. Rado,On Plateau’s Problem, Ann. of Math.31 (1930), 457–469. · JFM 56.0437.02
[12] M. Schiffer and N. S. Hawley,Connections and conformal mapping, Acta Math.107 (1962), 175–274. · Zbl 0115.29301
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.