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Original Articles

Constant Mean Curvature Surfaces with Two Ends in Hyperbolic Space

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Pages 101-119 | Published online: 03 Apr 2012

REFERENCES

  • Berglund , J. and Rossman , W. 1995 . “Minimal surfaces with catenoid ends” . Pacific J. Math. , 171 ( 2 ) : 353 – 371 . [Berglund and Rossman 1995]
  • Bryant , R. L. 1983–1984 . “Surfaces of mean curvature one in hyperbolic space”. ” . In Théorie des variétés minimales et applications 321 – 347 . Palaiseau [Bryant 1987], Astérisque 154–155, Soc. math. France, Paris, 1987
  • do Carmo , M. P. , Lawson , J. and Blaine , H. 1983 . “On Alexandrov-Bernstein theorems in hyperbolic space” . Duke Math. J. , 50 ( 4 ) : 995 – 1003 . [do Carmo and Lawson 1983]
  • do Carmo , M. P. , Gomes , J. and Thorbergsson , G. 1986 . “The influence of the boundary behaviour on hypersurfaces with constant mean curvature in Hn+1“ . Comment. Math. Helv. , 61 ( 3 ) : 429 – 441 . [do Carmo et al. 1986]
  • Hass , J. , Hutchings , M. and Schlafly , R. 1995 . “The double bubble conjecture” . Electron. Res. Announc. Amer. Math. Soc. , 1 ( 3 ) : 98 – 102 . [Hass et al. 1995]
  • Kapouleas , N. 1990 . “Complete constant mean curvature surfaces in Euclidean three-space” . Ann. of Math. (2) , 131 ( 2 ) : 239 – 330 . [Kapouleas 1990]
  • Karcher , H. 1989 . “The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions” . Manuscripta Math. , 64 ( 3 ) : 291 – 357 . [Karcher 1989]
  • Karcher , H. , Pinkall , U. and Sterling , I. 1988 . “New minimal surfaces in S3“ . J. Differential Geom. , 28 ( 2 ) : 169 – 185 . [Karcher et al. 1988]
  • Korevaar , N. J. , Kusner , R. and Solomon , B. 1989 . “The structure of complete embedded surfaces with constant mean curvature” . J. Differential Geom. , 30 ( 2 ) : 465 – 503 . [Korevaar et al. 1989]
  • Korevaar , N. J. , Kusner , R. , Meeks , I. , William , H. and Solomon , B. 1992 . “Constant mean curvature surfaces in hyperbolic space” . Amer. J. Math. , 114 ( 1 ) : 1 – 43 . [Korevaar et al. 1992]
  • Levitt , G. and Rosenberg , H. 1985 . “Symmetry of constant mean curvature hypersurfaces in hyperbolic space” . Duke Math. J. , 52 ( 1 ) : 53 – 59 . [Levitt and Rosenberg 1985]
  • Osserman , R. 1969 . A survey of minimal surfaces New York : Van Nostrand Reinhold Co. . [Osserman 1969], Reprinted by Dover Publications, New York, 1969
  • Polthier , K. 1990 . “New periodic minimal surfaces in H3“. ” . In Workshop on Theoretical and Numerical Aspects of Geometric Variational Problems 201 – 210 . Canberra [Polthier 1991], Dziuk, G. et al., Proc. Centre Math. Appl. Austral. Nat. Univ. 26, Austral. Nat. Univ., Canberra, 1991
  • Rossman , W. , Umehara , M. and Yamada , K. 1997 . “Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus” . Tohoku Math. J. , 49 : 449 – 484 . [Rossman et al. 1997]
  • Schoen , R. M. 1983 . “Uniqueness, symmetry, and embeddedness of minimal surfaces” . J. Differential Geom. , 18 ( 4 ) : 791 – 809 . [Schoen 1983]
  • Umehara , M. and Yamada , K. 1992 . “A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space” . J. Reine Angew. Math. , 432 : 93 – 116 . [Umehara and Yamada 1992]
  • Umehara , M. and Yamada , K. 1993 . “Complete surfaces of constant mean curvature 1 in the hyperbolic 3-space” . Ann. of Math. (2) , 137 ( 3 ) : 611 – 638 . [Umehara and Yamada 1993]
  • Umehara , M. and Yamada , K. 1996 . “Surfaces of constant mean curvature c in H3(–c2) with prescribed hyperbolic Gauss map” . Math. Ann. , 304 ( 2 ) : 203 – 224 . [Umehara and Yamada 1996]
  • Umehara , M. and Yamada , K. 1997 . “A duality on CMC-1 surfaces in hyperbolic space, and a hyperbolic analogue of the Osserman inequality” . Tsukuba J. Math. , 21 ( 1 ) : 229 – 237 . [Umehara and Yamada 1997]

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