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Demonstrates stable minimal tori in constant mean curvature manifolds, suggesting implications for Penrose inequalities.
In this paper we show how to replace hyperbolic cusps of a constant scalar curvature manifold with ends of infinite volume - funnels - keeping the scalar curvature constant and negative. This construction produces stable minimal tori belonging to a constant mean curvature foliation extending up to infinity. We discuss the relation of this construction with Penrose-type inequalities on time-symmetric relativistic initial data.
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Arezzo et al. (2026) studied this question.
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