Harmonic maps and asymptotic Teichmüller space |
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Authors: | Guowu Yao |
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Institution: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China |
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Abstract: | 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).
The work was supported by a Foundation for the Author of National Excellent Doctoral Dissertation (Grant No. 200518) of PR
China and the National Natural Science Foundation of China (Grant No. 10401036). |
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Keywords: | 58E20 37F30 |
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