manuscripta mathematica

, Volume 62, Issue 2, pp 249–256 | Cite as

New examples of harmonic diffeomorphisms of the hyperbolic plane onto itself

  • Hyeong In Choi
  • Andrejs Treibergs


A one parameter family of new examples of harmonic maps of the hyperbolic plane onto itself is constructed by studying the Gauss map of certain spacelike constant mean curvature surfaces in three dimensional Minkowski Space. These surfaces are obtained as surfaces of revolution. Explicit construction of the conformal diffeomorphism of the hyperbolic plane onto such surfaces gives a complete description of the boundary behavior of the harmonic maps.


Number Theory Algebraic Geometry Curvature Surface Topological Group Minkowski Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. AKUTAGAWA and S. NISHIKAWA: The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, preprint 1986Google Scholar
  2. [2]
    R. BARTNIK and L. SIMON: Spacelike hypersurfaces with prescribed boundary values and mean curvature, Commun. Math. Phys.87, 131–152 (1982)Google Scholar
  3. [3]
    H. I. CHOI and A. TREIBERGS: Gauss map of spacelike constant mean curvature hypersurfaces of Minkowski Space, preprint (1988)Google Scholar
  4. [4]
    J. HANO and K. NOMIZU: Surfaces of revolution with constant mean curvature in Lorentz-Minkowski Space, Tôhoku Math. J.,36, 427–437 (1984)Google Scholar
  5. [5]
    J. JOST: Harmonic maps between surfaces, Lecture Notes in Mathematics1062, Berlin Heidelberg New York: Springer-Verlag 1984Google Scholar
  6. [6]
    T. K. MILNOR: Harmonic maps and classical surface theory in Minkowski Space, Trans. Amer. Math Soc.280, 161–185 (1983)Google Scholar
  7. [7]
    E. RUH and J. VILMS: The tension field of the Gauss map, Trans. Amer. Math. Soc.149, 569–573 (1970)Google Scholar
  8. [8]
    R. SCHOEN and S.-T. YAU: On univalent harmonic maps between surfaces, Invent. Math.44, 265–278 (1978)Google Scholar
  9. [9]
    A. TREIBERGS: Entire Spacelike Hypersurfaces of constant mean curvature in Minkowski Space, Invent. Math.66, 39–56 (1982)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Hyeong In Choi
    • 1
    • 2
  • Andrejs Treibergs
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of IowaIowa City
  2. 2.Department of MathematicsUniversity of UtahSalt Lake City

Personalised recommendations