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Lipschitz continuity of harmonic maps between Alexandrov spaces

Hui-Chun Zhang Sun Yat-sen University Xi-Ping Zhu Sun Yat-sen University

Differential Geometry mathscidoc:1609.10096

Silver Award Paper in 2020

Invent. math., 211, (3), 863-934, 2018.3
In 1997, J. Jost [27] and F. H. Lin [39], independently proved that every energy minimizing harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov space with non-positive curvature is locally H¨older continuous. In [39], F. H. Lin proposed a challenge problem: Can the H¨older continuity be improved to Lipschitz continuity? J. Jost also asked a similar problem about Lipschitz regularity of harmonic maps between singular spaces (see Page 38 in [28]). The main theorem of this paper gives a complete resolution to it.
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@inproceedings{hui-chun2018lipschitz,
  title={Lipschitz continuity of harmonic maps between Alexandrov spaces},
  author={Hui-Chun Zhang, and Xi-Ping Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160910110448701208753},
  booktitle={Invent. math.},
  volume={211},
  number={3},
  pages={863-934},
  year={2018},
}
Hui-Chun Zhang, and Xi-Ping Zhu. Lipschitz continuity of harmonic maps between Alexandrov spaces. 2018. Vol. 211. In Invent. math.. pp.863-934. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160910110448701208753.
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