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arXiv · 1711.05245

Quantitative gradient estimates for harmonic maps into singular spaces

Hui-Chun Zhang·Xiao Zhong·Xi-Ping Zhu
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Abstract

In this paper, we will show the Yau's gradient estimate for harmonic maps into a metric space $(X,d_X)$ with curvature bounded above by a constant $\kappa$, $\kappa\geq0$, in the sense of Alexandrov. As a direct application, it gives some Liouville theorems for such harmonic maps. This extends the works of S. Y. Cheng [4] and H. I. Choi [5] to harmonic maps into singular spaces.

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Hui-Chun Zhang, Xiao Zhong, Xi-Ping Zhu. 2017-11-14. Quantitative gradient estimates for harmonic maps into singular spaces. https://arxiv.org/abs/1711.05245

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