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Rigidity of Teichmuller Space
Daskalopoulos, Georg...

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Rigidity of Teichmuller Space by Daskalopoulos, Georgios ( Author )
Lemonjar Open Access
N.A
11-02-2015
We prove the holomorphic rigidity conjecture of Teichmüller space which loosely speaking states that the action of the mapping class group uniquely determines the Teichmüller space as a complex manifold. The method of proof is through harmonic maps. We prove that the singular set of a harmonic map from a smooth n-dimensional Riemannian domain to the Weil-Petersson completion T¯¯¯¯ of Teichmüller space has Hausdorff dimension at most n−2, and moreover, u has certain decay near the singular set. Combining this with the earlier work of Schumacher, Siu and Jost-Yau, we provide a proof of the holomorphic rigidity of Teichmüller space. In addition, our results provide as a byproduct a harmonic maps proof of both the high rank and the rank one superrigidity of the mapping class group proved via other methods by Farb-Masur and Yeung.
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Article
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36.88 KB
English
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MYR 0.01
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http://arxiv.org/abs/1502.03367
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