Quantitative gradient estimates for harmonic maps into singular spaces

Hui-Chun Zhang Sun Yat-sen University Xiao Zhong University of Helsinki Xi-Ping Zhu Sun Yat-sen University

Differential Geometry mathscidoc:1908.10002

SCIENCE CHINA Mathematics
In this paper, we show the Yau’s gradient estimate for harmonic maps into a metric space (X, dX ) with curvature bounded above by a constant κ (κ 􏰣 0) in the sense of Alexandrov. As a direct application, it gives some Liouville theorems for such harmonic maps. This extends the works of Cheng (1980) and Choi (1982) to harmonic maps into singular spaces.
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@inproceedings{hui-chunquantitative,
  title={Quantitative gradient estimates for harmonic maps into singular spaces},
  author={Hui-Chun Zhang, Xiao Zhong, and Xi-Ping Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190816232401426284408},
  booktitle={SCIENCE CHINA Mathematics},
}
Hui-Chun Zhang, Xiao Zhong, and Xi-Ping Zhu. Quantitative gradient estimates for harmonic maps into singular spaces. In SCIENCE CHINA Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190816232401426284408.
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