Regularity of harmonic maps from polyhedra to CAT(1) spaces

Christine Breiner Department of Mathematics, Fordham University, Bronx, NY, 10458, USA Ailana Fraser Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada Lan-Hsuan Huang Department of Mathematics, University of Connecticut, Storrs, CT, 06269, USA Chikako Mese Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD, 21218, USA Pam Sargent Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada Yingying Zhang Yau Mathematical Science Center, Tsinghua University, Beijing, China

Differential Geometry mathscidoc:2204.10007

Calculus of Variations, 2017.12
We determine regularity results for energy minimizing maps from an n-dimensional Riemannian polyhedral complex X into a CAT(1) space. Provided that the metric on X is Lipschitz regular, we prove Hölder regularity with Hölder constant and exponent dependent on the total energy of the map and the metric on the domain. Moreover, at points away from the (n−2)-skeleton, we improve the regularity to locally Lipschitz. Finally, for points x ∈ X^{(k)} with k ≤ n−2, we demonstrate that the Hölder exponent depends on geometric and combinatorial data of the link of x ∈ X.
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@inproceedings{christine2017regularity,
  title={Regularity of harmonic maps from polyhedra to 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/20220428140128043578143},
  booktitle={Calculus of Variations},
  year={2017},
}
Christine Breiner, Ailana Fraser, Lan-Hsuan Huang, Chikako Mese, Pam Sargent, and Yingying Zhang. Regularity of harmonic maps from polyhedra to CAT(1) spaces. 2017. In Calculus of Variations. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428140128043578143.
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