# Dihedral rigidity for cubic initial data sets

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

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…

## 2 Citations

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In this paper we consider the positive mass theorem for general initial data sets satisfying the dominant energy condition which are singular across a piecewise smooth surface. We find jump…

### Rigid comparison geometry for Riemannian bands and open incomplete manifolds

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