## Rigidity of marginally outer trapped (hyper)surfaces with negative $\sigma$-constant

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## Abstract:

In this paper we generalize a result of Galloway and Mendes in two different situations: in the first case for marginally outer trapped surfaces (MOTSs) of genus greater than $1$ and, in the second case, for MOTSs of high dimension with negative $\sigma$-constant. In both cases we obtain a splitting result for the ambient manifold when it contains a stable closed MOTS which saturates a lower bound for the area (in dimension $2$) or for the volume (in dimension $\ge 3$). These results are extensions of theorems of Nunes and Moraru to general (non-time-symmetric) initial data sets.## References

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## Additional Information

**Abraão Mendes**- Affiliation: Instituto de Matemática, Universidade Federal de Alagoas, Maceió, Alagoas, Brazil
- Email: abraao.mendes@im.ufal.br
- Received by editor(s): September 21, 2016
- Received by editor(s) in revised form: November 11, 2018
- Published electronically: December 19, 2018
- Additional Notes: This work was carried out while the author was a Visiting Graduate Student at Princeton University during the 2015-2016 academic year. He was partially supported by NSF grant DMS-1104592 and by the CAPES Foundation, Ministry of Education of Brazil.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**372**(2019), 5851-5868 - MSC (2010): Primary 53C24
- DOI: https://doi.org/10.1090/tran/7752
- MathSciNet review: 4014296