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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Rigidity of marginally outer trapped (hyper)surfaces with negative $\sigma$-constant
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by Abraão Mendes PDF
Trans. Amer. Math. Soc. 372 (2019), 5851-5868 Request permission


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
  • Email:
  • 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:
  • MathSciNet review: 4014296