Abstract
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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