Methods and Applications of Analysis

Volume 21 (2014)

Number 3

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

DOI: http://dx.doi.org/10.4310/MAA.2014.v21.n3.a3

Authors

Xiaojing Chen (Department of Mathematics, University of California at Los Angeles)

Feng Guan (Department of Mathematics, University of California at Los Angeles)

Kefeng Liu (Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, China; and Department of Mathematics, University of California at Los Angeles)

Abstract

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.

Keywords

Teichmüller space, Calabi-Yau manifolds, global Torelli theorem

2010 Mathematics Subject Classification

14C30, 14C34, 32G05, 32G20, 32J25

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