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A Liouville-type theorem and Bochner formula for harmonic maps into metric spaces

Brian Freidin Department of Mathematics, Vancouver, British Columbia, Canada Yingying Zhang Yau Mathematical Sciences Center, Tsinghua University, Beijing, China

Differential Geometry mathscidoc:2204.10005

Communications in Analysis and Geometry, 28, (8), 1847-1862, 2021.1
We study analytic properties of harmonic maps from Riemannian polyhedra into CAT(κ) spaces for κ∈{0,1}. Locally, on each top-dimensional face of the domain, this amounts to studying harmonic maps from smooth domains into CAT(κ) spaces. We compute a target variation formula that captures the curvature bound in the target, and use it to prove an Lp Liouville-type theorem for harmonic maps from admissible polyhedra into convex CAT(κ) spaces. Another consequence we derive from the target variation formula is the Eells–Sampson Bochner formula for CAT(1) targets.
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@inproceedings{brian2021a,
  title={A Liouville-type theorem and Bochner formula for harmonic maps into metric spaces},
  author={Brian Freidin, and Yingying Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428135324267396141},
  booktitle={Communications in Analysis and Geometry},
  volume={28},
  number={8},
  pages={1847-1862},
  year={2021},
}
Brian Freidin, and Yingying Zhang. A Liouville-type theorem and Bochner formula for harmonic maps into metric spaces. 2021. Vol. 28. In Communications in Analysis and Geometry. pp.1847-1862. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428135324267396141.
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