Harmonic maps and asymptotic Teichmüller space

• Autores: Guowu Yao
• Localización: Manuscripta mathematica, ISSN 0025-2611, Vol. 122, Nº. 4, 2007, págs. 375-389
• Idioma: inglés
• DOI: 10.1007/s00229-007-0075-5
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• Resumen

  • 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).