A characterization of spherical polyhedral surfaces

Feng Luo

Geometric Analysis and Geometric Topology mathscidoc:1912.43796

Journal of Differential Geometry, 74, (3), 407-424, 2006
A spherical polyhedral surface is a triangulated surface obtained by isometric gluing of spherical triangles. For instance, the boundary of a generic convex polytope in the 3-sphere is a spherical polyhedral surface. This paper investigates these surfaces from the point of view of inner angles. A rigidity result is obtained. A characterization of spherical polyhedral surfaces in terms of the triangulation and the angle assignment is established.
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  title={A characterization of spherical polyhedral surfaces},
  author={Feng Luo},
  booktitle={Journal of Differential Geometry},
Feng Luo. A characterization of spherical polyhedral surfaces. 2006. Vol. 74. In Journal of Differential Geometry. pp.407-424. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205848071050360.
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