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A polyhedron comparison theorem for 3-manifolds with positive scalar curvature

Chao Li Princeton University

Differential Geometry mathscidoc:2105.10002

Inventiones mathematicae, 219, (1), 1-37, 2020.1
The study of comparison theorems in geometry has a rich history. In this paper, we establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collections of polyhedra with interior non-negative scalar curvature and mean convex faces, we prove the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding Euclidean model, unless it is a isometric to a flat polyhedron.
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@inproceedings{chao2020a,
  title={A polyhedron comparison theorem for 3-manifolds with positive scalar curvature},
  author={Chao Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210525045145595144833},
  booktitle={Inventiones mathematicae},
  volume={219},
  number={1},
  pages={1-37},
  year={2020},
}
Chao Li. A polyhedron comparison theorem for 3-manifolds with positive scalar curvature. 2020. Vol. 219. In Inventiones mathematicae. pp.1-37. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210525045145595144833.
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