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math.DG2025
Area-charge inequality and local rigidity in charged initial data sets
Abraão Mendes
This paper investigates the geometric consequences of equality in area-charge inequalities for spherical minimal surfaces and, more generally, for marginally outer trapped surfaces…
math.DG2025
Rigidity results for free boundary hypersurfaces in initial data sets with boundary
Deivid de Almeida, Abraão Mendes
In this work, we present several rigidity results for compact free boundary hypersurfaces in initial data sets with boundary. Specifically, in the first part of the paper, we exten…