Quantitative gradient estimates for harmonic maps into singular spaces

In this paper, we show the Yau’s gradient estimate for harmonic maps into a metric space ( X , d X ) 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 (19...

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Published in:Science China. Mathematics 2019-11, Vol.62 (11), p.2371-2400
Main Authors: Zhang, Hui-Chun, Zhong, Xiao, Zhu, Xi-Ping
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Language:English
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Applications of Mathematics
Mathematics
Mathematics and Statistics
Metric space
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description In this paper, we show the Yau’s gradient estimate for harmonic maps into a metric space ( X , d X ) 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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Mathematics and Statistics
Metric space
title Quantitative gradient estimates for harmonic maps into singular spaces
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