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Harmonic maps from a simplicial complex and geometric rigidity

Georgios Daskalopoulos Brown University Chikako Mese Johns Hopkins University

Differential Geometry mathscidoc:1609.10052

Journal of Differential Geometry, 78, (2), 269-293, 2008
We study harmonic maps from an admissible flat simplicial complex to a non-positively curved Riemannian manifold. Our main regularity theorem is that these maps are C1, at the interfaces of the top-dimensional simplices in addition to satisfying a balancing condition. If we assume that the domain is a 2-complex,then these maps are C1. As an application, we show that the regularity, the balancing condition and a Bochner formula lead to rigidity and vanishing theorems for harmonic maps. Furthermore, we give an explicit relationship between our techniques and those obtained via combinatorial methods.
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@inproceedings{georgios2008harmonic,
  title={HARMONIC MAPS FROM A SIMPLICIAL COMPLEX AND GEOMETRIC RIGIDITY},
  author={Georgios Daskalopoulos, and Chikako Mese},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909104548273246709},
  booktitle={Journal of Differential Geometry},
  volume={78},
  number={2},
  pages={269-293},
  year={2008},
}
Georgios Daskalopoulos, and Chikako Mese. HARMONIC MAPS FROM A SIMPLICIAL COMPLEX AND GEOMETRIC RIGIDITY. 2008. Vol. 78. In Journal of Differential Geometry. pp.269-293. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909104548273246709.
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