Methods and Applications of Analysis
Volume 21 (2014)
Special issue dedicated to the 60th birthday of Stephen S.-T. Yau: Part I
Guest editors: John Erik Fornæss, Norwegian University of Science and Technology; Xiaojun Huang, Rutgers University; Song-Ying Li, University of California, Irvine; Yat Sun Poon, University of California, Riverside; Wing Shing Wong, The Chinese University of Hong Kong; and Zhouping Xin, The Institute of Mathematical Sciences, CUHK.
Affine structures on Teichmüller spaces and applications
Pages: 313 – 336
We review our recent results on holomorphic affine structures on the Teichmüller spaces of Calabi-Yau manifolds and their Hodge metric completions, as well as their applications to global Torelli theorems for Calabi-Yau manifolds. As corollaries we show that the extended period map from the completion space is injective into the period domain, and that the completion space is a domain of holomorphy and admits a complete Kähler-Einstein metric.
Teichmüller space, Calabi-Yau manifolds, global Torelli theorem
2010 Mathematics Subject Classification
14C30, 14C34, 32G05, 32G20, 32J25