The classification of complete minimal surfaces with total curvature greater than $-12\pi$
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- by Francisco J. López
- Trans. Amer. Math. Soc. 334 (1992), 49-74
- DOI: https://doi.org/10.1090/S0002-9947-1992-1058433-9
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Abstract:
We classify complete orientable minimal surfaces with finite total curvature $- 8\pi$.References
- C. C. Chen and F. Gackstatter, Elliptic and hyperelliptic functions and complete minimal surfaces with handles, IME-USP 27 (1981).
C. J. Costa, Classification of complete minimal surfaces in ${{\mathbf {R}}^3}$ with total curvature $12\pi$, (preprint).
D. Hoffman and W. H. Meeks III, One parameter families of embedded minimal surfaces, (in preparation).
- David A. Hoffman and William Meeks III, A complete embedded minimal surface in $\textbf {R}^3$ with genus one and three ends, J. Differential Geom. 21 (1985), no. 1, 109–127. MR 806705
- 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. MR 683761, DOI 10.1016/0040-9383(83)90032-0 W. H. Meeks III, The classification of complete minimal surfaces in ${{\mathbf {R}}^3}$ with total curvature greater than $- 8\pi$ , Duke Math. J. 48 (1981). X. Mo and R. Osserman, On the Gauss map and total curvature of complete minimal surfaces and extension of Fujimoto’s theorem, (preprint).
- Robert Osserman, Global properties of minimal surfaces in $E^{3}$ and $E^{n}$, Ann. of Math. (2) 80 (1964), 340–364. MR 179701, DOI 10.2307/1970396
- Robert Osserman, A survey of minimal surfaces, 2nd ed., Dover Publications, Inc., New York, 1986. MR 852409
- Richard M. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geom. 18 (1983), no. 4, 791–809 (1984). MR 730928
- George Springer, Introduction to Riemann surfaces, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1957. MR 0092855 E. L. Barbanel, Complete minimal surfaces in ${{\mathbf {R}}^3}$ of low total curvature, Thesis, Univ. of Massachusetts, 1987. Yi Fang, Complete minimal surfaces of finite total curvature, Thesis, Univ. of Massachusetts, 1990.
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 334 (1992), 49-74
- MSC: Primary 53A10
- DOI: https://doi.org/10.1090/S0002-9947-1992-1058433-9
- MathSciNet review: 1058433