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This is a Quantitative Study study.

September 23, 2025Open Access

Marginally outer trap surface with capillary boundary and rigidity of initial data sets

Key Points

Estimates for the area of a marginally outer trap surface with capillary boundary were established.
Rigidity was proven for three-dimensional initial data sets with boundary under these conditions.
The results were extended to high-dimensional initial data sets using the Yamabe constant.
These findings contribute to the understanding of geometry and topology in various dimensions.

Abstract

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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Cite This Study

Sanghun Lee (Tue,) studied this question.

synapsesocial.com/papers/68d4759031b076d99fa6d631 https://doi.org/https://doi.org/10.48550/arxiv.2507.16617

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