Abstract: We show the rigidity of hyperbolic polyhedral metrics on 3-manifolds. By definition, such manifolds are isometric gluing of decorated hyperbolic tetrahedra. Here a decorated hyperbolic tetrahedron is a hyperbolic tetrahedron with only ideal or hyper-ideal vertices, and furthermore, with a horosphere called decoration centered at each ideal vertex. We show that the above hyperbolic polyhedral metric is determined up to isometry and change of decorations by its curvature.
This work generalized Luo-Yang's rigidity results [2018, J. Topol.] to the most general situation.
This is joint work with Ke Feng and Chunlei Liu.
