Calculus of Variations and Geometric Measure Theory
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E. Le Donne - A. Ottazzi - B. Warhurst

Ultrarigid tangents of sub-Riemannian nilpotent groups

created by ledonne on 15 Apr 2011

[BibTeX]

Preprint

Inserted: 15 apr 2011

Year: 2011

Abstract:

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.

Keywords: Carnot groups, Quasiconformal maps, Metric tangents, Nilpotent groups


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