Existence of harmonic maps into CAT(1) spaces

Christine Breiner Department of Mathematics, Fordham University, Bronx, New York, U.S.A. Ailana Fraser Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada Lan-Hsuan Huang Department of Mathematics, University of Connecticut, Storrs, Ct., U.S.A. Chikako Mese Department of Mathematics, Johns Hopkins University, Baltimore, Maryland, U.S.A. Pam Sargent Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada Yingying Zhang Yau Mathematical Science Center, Tsinghua University, Beijing, China

Differential Geometry mathscidoc:2204.10006

Communications in Analysis and Geometry, 28, (4), 781-835, 2020.10
Let φ∈C^0∩W_{1,2}(Σ,X) where Σ is a compact Riemann surface, X is a compact locally CAT(1) space, and W_{1,2}(Σ,X) is defined as in Korevaar-Schoen. We use the technique of harmonic replacement to prove that either there exists a harmonic map u: Σ → X homotopic to φ or there exists a nontrivial conformal harmonic map v: S^2 → X. To complete the argument, we prove compactness for energy minimizers and a removable singularity theorem for conformal harmonic maps.
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@inproceedings{christine2020existence,
  title={Existence of harmonic maps into CAT(1) spaces},
  author={Christine Breiner, Ailana Fraser, Lan-Hsuan Huang, Chikako Mese, Pam Sargent, and Yingying Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428135654105186142},
  booktitle={Communications in Analysis and Geometry},
  volume={28},
  number={4},
  pages={781-835},
  year={2020},
}
Christine Breiner, Ailana Fraser, Lan-Hsuan Huang, Chikako Mese, Pam Sargent, and Yingying Zhang. Existence of harmonic maps into CAT(1) spaces. 2020. Vol. 28. In Communications in Analysis and Geometry. pp.781-835. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428135654105186142.
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