Rigidity of minimal submanifolds in hyperbolic space

Details Rigidity of minimal submanifolds in hyperbolic space Rigidity of minimal submanifolds in hyperbolic space

2010-02-20

arxiv.org/abs/1002.3885v1

Archiv der Mathematik, 94 (2010), 173-181

Mathematics

Differential Geometry

Scientific paper

10.1007/s00013-009-0096-2

We prove that if an $n$-dimensional complete minimal submanifold $M$ in
hyperbolic space has sufficiently small total scalar curvature then $M$ has
only one end. We also prove that for such $M$ there exist no nontrivial $L^2$
harmonic 1-forms on $M$.

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