This analysis reveals rigidity in initial data sets with marginally outer trap surfaces, suggesting broader implications in geometry.
In this paper, we present the several rigidity results of initial data sets with boundary when a marginally outer trap surface (MOTS) with capillary boundary is embedded. First, we establish estimates for the area of a MOTS with capillary boundary. Next, we prove a rigidity for 3-dimensional initial data sets with boundary. Furthermore, we extend our results from the 3-dimensional case to the high dimensional initial data sets using the Yamabe constant.
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Sanghun Lee (2025) studied this question.
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