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Doubly-connected minimal surfaces. (English) Zbl 0352.53005


MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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[1] Alexander, H., & R. Osserman, Area bounds for various classes of surfaces. Amer. J. Math. (to appear). · Zbl 0326.53030
[2] Alexander, H., D. Hoffman, & R. Osserman, Area estimates for submanifolds of euclidean space, INDAM Symposia Mathematica. XIV, 445-455. ?monograf?, Bologna, 1974. · Zbl 0326.53029
[3] Bailyn, P.M., Doubly-connected minimal surfaces. Trans. Amer. Math. Soc. 128, 206-220 (1967) · Zbl 0168.42305 · doi:10.1090/S0002-9947-1967-0211333-1
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[5] Gulliver, R., R. Osserman, O. Royden, A theory of branched immersions of surfaces. Amer. J. Math. 95, 750-812 (1973). · Zbl 0295.53002 · doi:10.2307/2373697
[6] Hildebrandt, S., Maximum principles for minimal surfaces and for surfaces of continuous mean Curvature. Math. Z. 128, 157-173 (1972). · Zbl 0253.53005 · doi:10.1007/BF01111709
[7] Kaul, H., Isoperimetrische Ungleichung und Gauss-Bonnet Formel für H-Flächen in RiemannSchen Mannigfaltigkeiten. Arch. Rational Mech. Anal. 45, 194-221 (1972) · Zbl 0234.53054 · doi:10.1007/BF00281532
[8] Kaul, H., Remarks on the isoperimetric inequality for multiply-connected H-surfaces. Math. Z. 128, 271-276 (1972) · Zbl 0242.53001 · doi:10.1007/BF01111710
[9] Nitsche, J.C.C., A necessary criterion for the existence of certain minimal surfaces. J. Math. Mech. 13, 659-666 (1964) · Zbl 0168.42304
[10] Nitsche, J.C.C., A supplement to the conditions of J. Douglas. Rend. Circ. Mat. Palermo 13, 192-198 (1964) · Zbl 0136.16702 · doi:10.1007/BF02849527
[11] Nitsche, J.C.C., The isoperimetric inequality for multiply-connected minimal surfaces. Math. Ann. 160, 370-375 (1965) · Zbl 0144.20505 · doi:10.1007/BF01360908
[12] Nitsche, J.C.C., Note on the nonexistence of minimal surfaces. Proc. Amer. Math. Soc. 19, 1303-1305 (1968) · Zbl 0167.11402 · doi:10.1090/S0002-9939-1968-0234365-2
[13] Nitsche, J.C.C., & J. Leavitt, Numerical estimates for minimal surfaces. Math. Ann. 180, 170-174 (1969) · Zbl 0164.52203 · doi:10.1007/BF01350745
[14] Osserman, R., A Survey of Minimal Surfaces. Van Nostrand-Reinhold, New York, 1969. · Zbl 0209.52901
[15] Osserman, R., Isoperimetric and related inequalities. Proc. 20th A.M.S. Summer Math. Inst., held at Stanford, Calif., August 1973 (to apear).
[16] Osserman, R., Variations on a theme of Plateau. pp. 65-74 of Global Analysis and Its Applications, III; Lectures Presented at Centre for Theoretical Physics, Trieste, 4 July?25 August 1972. International Atomic Energy Agency, Vienna, 1974.
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