Tohoku Mathematical Journal

Weierstrass representation for minimal surfaces in hyperbolic space

Masatoshi Kokubu

Full-text: Open access

Article information

Tohoku Math. J. (2) Volume 49, Number 3 (1997), 367-377.

First available in Project Euclid: 3 May 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]


Kokubu, Masatoshi. Weierstrass representation for minimal surfaces in hyperbolic space. Tohoku Math. J. (2) 49 (1997), no. 3, 367--377. doi:10.2748/tmj/1178225110.

Export citation


  • [B] R. BRYANT, Surfaces of mean curvature one in hyperbolic space, Asterisque 154-155 (1987), 321-347.
  • [D-D] M. DO CARMO AND M. DAJCZER, Rotational hypersurfaces in spaces of constant curvature, Trans Amer. Math. Soc. 277 (1983), 685-709.
  • [E] CH. L. EPSTEIN, The hyperbolic Gauss map and quasiconformal reflections, J. Reine Angew Math. 372 (1986), 96-135.
  • [G-O-R] R. D. GULLIVER, II, R. OSSERMAN AND H. L. ROYDON, A theory of branched immersions o surfaces, Amer. J. Math. 95 (1973), 750-812.
  • [K] K. KENMOTSU, Weierstrass formula for surfaces of prescribed mean curvature, Math. Ann. 24 (1979), 89-99.
  • [O] M. OBATA, The Gauss map of immersions of Riemannian manifoldsin space of constant curvature, J. Differential Geom. 2 (1968), 217-223.
  • [U] K. UHLENBECK, Harmonic maps into Lie groups (classical solutions of the chiral model), J. Differential Geom. 30 (1989), 1-50.
  • [U-Y] M. UMEHARA AND K. YAMADA, Complete surfaces of constant mean curvature one in th hyperbolic 3-space, Ann.of Math, 137 (1993), 611-638.