Duke Mathematical Journal

The geometry of properly embedded special surfaces in $\mathbf{R}^3$; e.g., surfaces satisfying $aH+bK=1$, where $a$ and $b$ are positive

Harold Rosenberg and Ricardo Sa Earp
Source: Duke Math. J. Volume 73, Number 2 (1994), 291-306.
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Primary Subjects: 53A10
Secondary Subjects: 49Q05
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288813
Mathematical Reviews number (MathSciNet): MR1262209
Zentralblatt MATH identifier: 0802.53002
Digital Object Identifier: doi:10.1215/S0012-7094-94-07314-6

References

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Digital Object Identifier: doi:10.2307/2032934
[3] R. Earp, F. Brito, W. Meeks, and H. Rosenberg, Structure theorems for constant mean curvature surfaces bounded by a planar curve, Indiana Math. J. 40 (1991), no. 1, 333–343.
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Project Euclid: euclid.jdg/1214436094
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Project Euclid: euclid.jdg/1214442008
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Mathematical Reviews (MathSciNet): MR90g:53011
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[7] N. Kapouleas, Complete constant mean curvature surfaces in Euclidean three space, Ann. of Math. (2) 131 (1990), no. 2, 239–330.
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[8] P. Hartman and A. Wintner, Umbilical points and $W$-surfaces, Amer. J. Math. 76 (1954), 502–508.
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[10] H. Hopf, Differential Geometry in the Large, Lecture Notes in Math., vol. 1000, Springer-Verlag, Berlin, 1983.
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[11] H. Rosenberg, Hypersurfaces of constant curvature in space forms, Bull. Sci. Math. 117 (1993), no. 2, 211–239.
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[12] F. Brito and R. S. Earp, On the structure of certain Weingarten surfaces with boundary a circle, preprint.
[13] H. Rosenberg and R. Sa Earp, Some structure theorems for complete constant mean curvature surfaces with boundary a convex curve, Proc. Amer. Math. Soc. 113 (1991), no. 4, 1045–1053.
Mathematical Reviews (MathSciNet): MR92c:53003
Zentralblatt MATH: 0748.53003
Digital Object Identifier: doi:10.2307/2048783

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