Convergence of an iterative algorithm for Teichm\" uller maps via generalized harmonic maps

Lui Lok Ming Gu Xianfeng Shing-Tung Yau

Geometric Analysis and Geometric Topology mathscidoc:1912.43694

arXiv preprint arXiv:1307.2679, 2013.7
Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichm ller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal Teichm ller map between Riemann surfaces of finite type are theoretically guaranteed [1]. Recently, a simple iterative algorithm for computing the Teichm ller maps between connected Riemann surfaces with given boundary value was proposed in [11]. Numerical results was reported in the paper to show the effectiveness of the algorithm. The method was successfully applied to landmark-matching registration. The purpose of this paper is to prove the iterative algorithm proposed in [11] indeed converges.
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@inproceedings{lui2013convergence,
  title={Convergence of an iterative algorithm for Teichm\" uller maps via generalized harmonic maps},
  author={Lui Lok Ming, Gu Xianfeng, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205030162239258},
  booktitle={arXiv preprint arXiv:1307.2679},
  year={2013},
}
Lui Lok Ming, Gu Xianfeng, and Shing-Tung Yau. Convergence of an iterative algorithm for Teichm\" uller maps via generalized harmonic maps. 2013. In arXiv preprint arXiv:1307.2679. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205030162239258.
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