Rigidity of marginally outer trapped (hyper)surfaces with negative ๐-constant
Abraรฃo Mendes
Source 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 1 and, in the second case, for MOTSs of high dimension with negative ฯ \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 2 ) or for the volume (in dimension โฅ 3 \ge 3 ). These results are extensions of theorems of Nunes and Moraru to general (non-time-symmetric) initial data sets.
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