2016/09/06 by Mendes, Abraão
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1609.01579
In this paper we generalize the main result of [13] in two different situations: in the first case for MOTSs of genus greater than one and, in the second case, for MOTSs of high dimension with negative σ-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 ≥3). These results are extensions of [21, Theorem 3] and [20, Theorem 3] to general (non-time-symmetric) initial data sets.