Complete embedded minimal surfaces of finite total curvature. (English) Zbl 0566.53017
This is a short announcement of the results described in the preceding review.
Reviewer: Bernd Wegner
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
Citations:
Zbl 0566.53016References:
| [1] | C. Costa, Imersões minimas completas em R3 de gênero um e curvatura total finita, Doctoral thesis, IMPA, Rio de Janeiro, Brasil, 1982. |
| [2] | David A. Hoffman and Robert Osserman, The geometry of the generalized Gauss map, Mem. Amer. Math. Soc. 28 (1980), no. 236, iii+105. · Zbl 0469.53004 · doi:10.1090/memo/0236 |
| [3] | Luquésio P. Jorge and William H. Meeks III, The topology of complete minimal surfaces of finite total Gaussian curvature, Topology 22 (1983), no. 2, 203 – 221. · Zbl 0517.53008 · doi:10.1016/0040-9383(83)90032-0 |
| [4] | Robert Osserman, Global properties of minimal surfaces in \?³ and \?\(^{n}\), Ann. of Math. (2) 80 (1964), 340 – 364. · Zbl 0134.38502 · doi:10.2307/1970396 |
| [5] | Richard M. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geom. 18 (1983), no. 4, 791 – 809 (1984). · Zbl 0575.53037 |
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