Ultrarigid tangents of sub-Riemannian nilpotent groups

Details Ultrarigid tangents of sub-Riemannian nilpotent groups Ultrarigid tangents of sub-Riemannian nilpotent groups

2011-04-15

arxiv.org/abs/1104.3071v1

Mathematics

Metric Geometry

Scientific paper

We show that the tangent cone at the identity is not a complete quasiconformal invariant for sub-Riemannian nilpotent groups. Namely, we show that there exists a nilpotent Lie group equipped with left invariant sub-Riemannian metric that is not locally quasiconformally equivalent to its tangent cone at the identity. In particular, such spaces are not locally bi-Lipschitz homeomorphic. The result is based on the study of Carnot groups that are rigid in the sense that their only quasiconformal maps are the translations and the dilations.

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