Stable embedded minimal surfaces bounded by a straight line

Calculus of Variations and Partial Differential Equations

Volumn 29, Issue 2, 2007, Pages 267-279

  Pérez, Joaquín ^a  

^a UNIVERSITY OF GRANADA   (Spain)

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[No Author keywords available]

Indexed keywords

EID: 33947703016     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-006-0069-2     Document Type: Article

References (20)

1. Alt, H.W.: Verzweigungspunkte von H-Flächen (I). Math. Z. 127, 333-362 (1972). MR0312404, Zbl 0253.58007
2. Alt, H.W.: Verzweigungspunkte von H-Flächen (II). Math. Ann. 201, 33-55 (1973). MR0331195, Zbl 0257.58005
3. 3 are planes. Bull. AMS. 1, 903-906 (1979). MR0546314, Zbl 442.53013
4. Douglas, J.: Minimal surfaces of higher topological structure. Ann. Math. 40, 205-298 (1939). MR1503457, Zbl 0020.37402
5. Finn, R.: Remarks relevant to minimal surfaces, and to surfaces of prescribed mean curvature. J. Anal. Math. 14, 139-160 (1965). MR0188909, Zbl 0163.34604
6. Fischer-Colbrie, D., Schoen, R.: The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature. Comm. Pure Appl. Math. 33, 99-211 (1980). MR0562550, Zbl 439.53060
7. Fleming, W.H.: On the oriented Plateau problem. Rend. Circ. Mat. Palermo 11(2), 69-90 (1962). MR0157263, Zbl 01.07.31304
8. Gulliver, R.: Regularity of minimizing surfaces of prescribed mean curvature. Ann. Math. 97, 275-305 (1973). MR0317188, Zbl 0246.53053
9. Gulliver, R., Lesley, F.: On boundary branch points of minimizing surfaces. Arch. Rational Mech. Anal. 52, 20-25 (1973). MR0346641, Zbl 0263.53009
10. Hardt, R., Simon, L.: Boundary regularity and embedded minimal solutions for the oriented Plateau problem. Ann. Math. 110, 439-486 (1979). MR0554379, Zbl 0457.49029
11. Heinz, E., Hildebrandt, S.: The number of branch points of surfaces of bounded mean curvature. J. Differ. Geom. 55(4), 227-235 (1970). MR0267495, Zbl 0195.23003
12. Hoffman, D., Meeks III. W.H.: The strong halfspace theorem for minimal surfaces. Invent. Math. 101, 373-377 (1990). MR1062966, Zbl 722.53054
13. 3 bounds a unique area-minimizing surface. Invent. Math. 45, 253-297 (1978). MR0513662, Zbl 0378.49028
14. Morgan, F.: A Beginner's Guide to Geometric Measure Theory. Academic Press, New York (1987)
15. Osserman, R.: A proof of the regularity everywhere to Plateau's problem. Ann. Math. 91(2), 550-569 (1970). MR0266070, Zbl 0194.22302
16. Osserman, R.: A Survey of Minimal Surfaces, 2nd edn. Dover Publications, New York (1986). MR0852409, Zbl 0209.52901
17. Rado, T.: On Plateau's problem. Ann. Math. 31(3), 457-469 (1930). MR1502955
18. Schoen, R.: Estimates for Stable Minimal Surfaces in Three Dimensional Manifolds, vol. 103 of Annals of Math. Studies. Princeton University Press, Princeton (1983). MR0795231, Zbl 532.53042
19. White, B.: Existence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on 3-manifolds. J. Diff. Geom. 33(2), 413-443 (1991). MR1094464, Zbl 0737.53009
20. White, B.: Half of Enneper's surface minimizes area. In: Jost, J. (ed.) Geometric Analysis and the Calculus of Variations for Stefan Hildebrandt, pp 361-368. International Press, Somerville (1996). MR1449416, Zbl 1039.53018