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arXiv · 1104.3071

Ultrarigid tangents of sub-Riemannian nilpotent groups

Enrico Le Donne·Alessandro Ottazzi·Ben Warhurst
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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.

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BibTeXRIS

Enrico Le Donne, Alessandro Ottazzi, Ben Warhurst. 2011-04-15. Ultrarigid tangents of sub-Riemannian nilpotent groups. https://arxiv.org/abs/1104.3071

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