Location of Repository

Harmonic diffeomorphisms of noncompact surfaces and Teichmüller spaces

By V. (Vladimir) Markovic


Let g : M -> N be a quasiconformal harmonic diffeomorphism between noncompact Riemann surfaces M and N. In this paper we study the relation between the map g and the complex structures given on M and N. In the case when M and N are of finite analytic type we derive a precise estimate which relates the map g and the Teichmüller distance between complex structures given on M and N. As a corollary we derive a result that every two quasiconformally related finitely generated Kleinian groups are also related by a harmonic diffeomorphism. In addition, we study the question of whether every quasisymmetric selfmap of the unit circle has a quasiconformal harmonic extension to the unit disk. We give a partial answer to this problem. We show the existence of the harmonic quasiconformal extensions for a large class of quasisymmetric maps. In particular it is proved that all symmetric selfmaps of the unit circle have a unique quasiconformal harmonic extension to the unit disk

Topics: QA
Publisher: Cambridge University Press
Year: 2002
OAI identifier: oai:wrap.warwick.ac.uk:783

Suggested articles



  1. 114 noncompact surfaces and teichm¨ uller spaces
  2. (1969). A bundle description of Teichmuller theory',
  3. (1979). A new proof of a fundamental inequality for quasiconformal mappings', doi
  4. (1997). Compact Riemann surfaces (Springer, doi
  5. (1992). Constant mean curvature surface, harmonic maps and universal Teichm¨ uller space',
  6. (1987). Global analysis and Teichm¨ uller theory',
  7. (1994). Harmonic dieomorphisms of the hyperbolic plane', doi
  8. (1991). In energy harmonic maps and degeneration of hyperbolic surfaces in moduli space', doi
  9. (1997). Lectures on harmonic maps', doi
  10. (1966). Lectures on quasiconformal mappings doi
  11. (1999). New version of the main inequality and uniqueness of harmonic maps',
  12. (1967). On mappings conformal at the boundary', doi
  13. (1969). On quasiconformal mappings which keep the boundary points doi
  14. (1997). On the boundary value problem for harmonic maps of the Poincar e disk',
  15. (1976). On the existence of extremal Teichm¨ uller mappings', doi
  16. (1978). On univalent harmonic maps between surfaces', doi
  17. private communication. doi
  18. (1995). Quasiconformal harmonic dieomorphism and the universal Teichm¨ uller space',
  19. (1982). Quasiconformal mapping with free boundary components', doi
  20. (1973). Quasiconformal mappings in the plane (Springer, doi
  21. (1978). Some properties and applications of harmonic mappings', doi
  22. (1992). Symmetric structures on a closed curve', doi
  23. (1987). Teichm¨ uller theory and quadratic dierentials
  24. The role of harmonic mappings in rigidity and deformation problems', preprint,
  25. (1998). The Teichm¨ uller space of a holomorphic dynamical system',
  26. (1989). The Teichm¨ uller theory of harmonic maps', doi
  27. (1981). Ueber extremale quasikonforme Abbildungen, doi
  28. (2000). Uniformly bounded maximal -disks, Bers spaces and harmonic maps',
  29. (1993). Uniqueness and regularity of proper harmonic maps', doi
  30. (1986). Univalent functions and Teichm¨ uller spaces (Springer,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.