manuscripta mathematica

, Volume 122, Issue 4, pp 375–389

Harmonic maps and asymptotic Teichmüller space


DOI: 10.1007/s00229-007-0075-5

Cite this article as:
Yao, G. manuscripta math. (2007) 122: 375. doi:10.1007/s00229-007-0075-5


In this paper, the asymptotic boundary behavior of a Hopf differential or the Beltrami coefficient of a harmonic map is investigated and certain compact properties of harmonic maps are established. It is shown that, if f is a quasiconformal harmonic diffeomorphism between two Riemann surfaces and is homotopic to an asymptotically conformal map modulo boundary, then f is asymptotically conformal itself. In addition, we prove that the harmonic embedding map from the Bers space B Q D (X) of an arbitrary hyperbolic Riemann surface X to the Teichmüller space T (X) induces an embedding map from the asymptotic Bers space A B Q D (X), a quotient space of B Q D (X), into the asymptotic Teichmüller space AT (X).

Mathematics Subject Classification (2000)

58E20 37F30 

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingPeople’s Republic of China