Convergence of harmonic maps on the Poincaré disk |
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| Authors: | Guowu Yao |
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| Affiliation: | School of Mathematical Sciences, Peking University, Beijing, 100871, People's Republic of China |
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| Abstract: | Let  be a sequence of locally quasiconformal harmonic maps on the unit disk  with respect to the Poincaré metric. Suppose that the energy densities of  are uniformly bounded from below by a positive constant and locally uniformly bounded from above. Then there is a subsequence of  that locally uniformly converges on  , and the limit function is either a locally quasiconformal harmonic map of the Poincaré disk or a constant. Especially, if the limit function is not a constant, the subsequence can be chosen to satisfy some stronger conditions. As an application, it is proved that every point of the space  , a subspace of the universal Teichmüller space, can be represented by a quasiconformal harmonic map that is an asymptotic hyperbolic isometry. |
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| Keywords: | Harmonic map energy density locally quasiconformal map asymptotic hyperbolic isometry |
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