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.
From Cusps to Funnels of constant scalar curvature and CMC submanifolds / Arezzo, C., Lancini, S., Mazzieri, L.. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 177:4(2026). [10.1007/s00229-026-01723-5]
From Cusps to Funnels of constant scalar curvature and CMC submanifolds
Mazzieri, Lorenzo
2026-01-01
Abstract
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.File in questo prodotto:
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