Lipschitz continuity of harmonic maps between Alexandrov spaces

Hui-Chun Zhang; Xi-Ping Zhu

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arXiv · 1311.1331

Lipschitz continuity of harmonic maps between Alexandrov spaces

Hui-Chun Zhang·Xi-Ping Zhu

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Abstract

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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Hui-Chun Zhang, Xi-Ping Zhu. 2013-11-06. Lipschitz continuity of harmonic maps between Alexandrov spaces. https://arxiv.org/abs/1311.1331

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