Conformal geometry and complete minimal surfaces
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- by Rob Kusner PDF
- Bull. Amer. Math. Soc. 17 (1987), 291-295
References
- Thomas F. Banchoff, Triple points and surgery of immersed surfaces, Proc. Amer. Math. Soc. 46 (1974), 407–413. MR 377897, DOI 10.1090/S0002-9939-1974-0377897-1
- Robert L. Bryant, A duality theorem for Willmore surfaces, J. Differential Geom. 20 (1984), no. 1, 23–53. MR 772125 3. R. Bryant, Personal communication, 1985. 4. C. Costa, Imersões minimas completas em R, Doctoral thesis, IMPA, Rio de Janeiro, Brasil, 1982. 5. G. Francis, Some equivariant eversions of the sphere (privately circulated manuscript), 1977.
- David A. Hoffman and William H. Meeks III, Complete embedded minimal surfaces of finite total curvature, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 1, 134–136. MR 766971, DOI 10.1090/S0273-0979-1985-15318-2
- 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 8. R. Kusner, Complete minimal surfaces by minimizing ∫ H2 (lecture notes), 1984.
- Rob Kusner, Comparison surfaces for the Willmore problem, Pacific J. Math. 138 (1989), no. 2, 317–345. MR 996204, DOI 10.2140/pjm.1989.138.317 10. H. B. Lawson, Lectures on minimal submanifolds. I, Publish or Perish, Berkeley, 1980.
- Peter Li and Shing Tung Yau, A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Invent. Math. 69 (1982), no. 2, 269–291. MR 674407, DOI 10.1007/BF01399507
- William H. Meeks III, The classification of complete minimal surfaces in $\textbf {R}^{3}$ with total curvature greater than $-8\pi$, Duke Math. J. 48 (1981), no. 3, 523–535. MR 630583
- Robert Osserman, On complete minimal surfaces, Arch. Rational Mech. Anal. 13 (1963), 392–404. MR 151907, DOI 10.1007/BF01262706
- Richard M. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geom. 18 (1983), no. 4, 791–809 (1984). MR 730928 15. M. Spivak, A comprehensive introduction to differential geometry. IV, Publish or Perish, Berkeley, 1975. 16. D. Hoffman and W. Meeks III, The classical theory of minimal surfaces (in preparation).
- Nicholas J. Korevaar, Rob Kusner, and Bruce Solomon, The structure of complete embedded surfaces with constant mean curvature, J. Differential Geom. 30 (1989), no. 2, 465–503. MR 1010168
Additional Information
- Journal: Bull. Amer. Math. Soc. 17 (1987), 291-295
- MSC (1985): Primary 53A10, 49F10, 57R42
- DOI: https://doi.org/10.1090/S0273-0979-1987-15564-9
- MathSciNet review: 903735