• Corpus ID: 237259928

Dihedral rigidity for cubic initial data sets

@inproceedings{Tsang2021DihedralRF,
  title={Dihedral rigidity for cubic initial data sets},
  author={Tin-Yau Tsang},
  year={2021}
}

• Tin-Yau Tsang
• Published 19 August 2021
• Mathematics

In this paper we pose and prove a spacetime version of Gromov’s dihedral rigidity theorem ([17],[24],[25]) for cubes when the dimension is 3 by studying the level sets of spacetime harmonic functions ([40],[7],[21]), extending the work of [9]. As a corollary, we also obtain an alternative proof of dihedral rigidity for prisms in hyperbolic space ([26]). We then discuss the relation between polyhedra and the spacetime positive mass theorem. This generalises the work of [32] and [25]. Finally, we show dihedral rigidity of charged Riemannian cubes by charged harmonic functions ([6]).