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Initial data set rigidity results for polyhedra

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arxiv 2408.13801 v1 pith:T5BPGTSZ submitted 2024-08-25 math.DG gr-qc

Xiaoxiang Chai (POSTECH) , Xueyuan Wan (CQUT) This is my paper · ORCID
classification math.DGgr-qc
keywords rigiditydatadihedralinitialmasspositivespacetimetheorem
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Using spinors, we show a dihedral type rigidity for polyhedral initial data sets. This rigidity connects spacetime positive mass theorem, dihedral rigidity and capillary marginally trapped surfaces. Our method is to extend the rigidity analysis of spacetime positive mass theorem due to Beig-Chrusciel to the settings of a twisted spinor bundle.

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  1. Marginally outer trap surface with capillary boundary and rigidity of initial data sets

    math.DG 2025-07 reject novelty 6.0 of 10

    For stable MOTS with capillary boundary, equality in the area estimate forces the contact angle to 90 degrees and the ambient initial data set to split as a product, under stated energy assumptions.

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