Rigidity of Teichmüller space
Rigidity of Teichmüller space
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DOI：
10.1007/s00222-020-01020-2
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发表时间：
2015-02
影响因子：
3.1
通讯作者：
Georgios Daskalopoulos;Chikako Mese
中科院分区：
文献类型：
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作者：
Georgios Daskalopoulos;Chikako Mese
证明了Teichmüler空间的全纯刚性猜想，广义地说，映射类群的作用唯一地决定了Teichmüler空间是一个复流形。证明的方法是通过调和映射。证明了Teichmüler空间中从光滑Riemannian区域到Weil-Petersson完备化的调和映射的奇异集至多有Hausdorff维，并且u在奇异集附近有一定的衰减性。结合Schumacher，Siu和Jost-Yau的早期工作，我们给出了Teichmüler空间的全纯刚性的一个证明。此外，作为副产品，我们的结果提供了由Farb-Masur和Yeung用其他方法证明的映射类群的高阶和一阶超刚性的调和映射的证明。
We prove theholomorphic rigidity conjecture of Teichmüller spacewhich 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 smoothn-dimensional Riemannian domain to the Weil–Petersson completionof Teichmüller space has Hausdorff dimension at most, and moreover,uhas 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.