Rigidity of stable cylinders in three-manifolds

Details Rigidity of stable cylinders in three-manifolds Rigidity of stable cylinders in three-manifolds

2011-04-16

arxiv.org/abs/1104.3252v1

Mathematics

Differential Geometry

Scientific paper

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 {\it bifurcation phenomena}, 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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