Liouville theorems for harmonic maps into $\operatorname {CAT}(1)$ spaces

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发表日期：

2025年3月13日

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Qun Chen,
Jie Wang

摘要

We prove Liouville theorems for harmonic maps into metric spaces with curvature bounded above by a constant $k>0$ $k > 0$ in the sense of Alexandrov. Our results generalize a Liouville theorem for harmonic maps from manifolds with non-negative Ricci curvature into $\operatorname {CAT}(1)$ $CAT (1)$ space in the recent work (Zhang et al. in Sci China Math 62(11): 2371–2400, 2019) of Zhang-Zhong-Zhu. As a direct corollary, we improve a well-known result of Choi (Proc Amer Math Soc 85(1): 91–94, 1982) for harmonic maps between smooth Riemannian manifolds.

Liouville theorems for harmonic maps into \(\operatorname {CAT}(1)\) spaces

摘要