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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Author: Abraão Mendes
Journal: Trans. Amer. Math. Soc. 372 (2019), 5851-5868
MSC (2010): Primary 53C24
Published electronically: December 19, 2018
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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.

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Additional Information

Abraão Mendes
Affiliation: Instituto de Matemática, Universidade Federal de Alagoas, Maceió, Alagoas, Brazil

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.
Article copyright: © Copyright 2018 American Mathematical Society