Rigidity of stable cylinders in three-manifolds

Espinar, José

doi:10.1090/S0002-9939-2011-11197-3

Rigidity of stable cylinders in three-manifolds
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Proc. Amer. Math. Soc. 140 (2012), 1769-1775 Request permission

Abstract:

In this paper we show how the existence of a certain stable cylinder determines (locally) the ambient manifold where it is immersed. This cylinder has to verify a bifurcation phenomenon; we make this explicit in the introduction. In particular, the existence of such a stable cylinder implies that the ambient manifold has infinite volume.

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