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Sibirsk. Mat. Zh., 2014, Volume 55, Number 5, Pages 1091–1103 (Mi smj2590)  

The Liouville theorem for conformal mappings on Carnot groups with Goursat–Darboux distribution

D. V. Isangulova

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: Under minimal assumptions on smoothness we prove the Liouville theorem on conformal mappings for one infinite series of Carnot groups $\mathbb J^k$ with sub-Riemannian metric with Goursat–Darboux distribution, $k\ge2$: each mapping with $1$-bounded distortion of a connected domain $U$ on $\mathbb J^k$ is equal to the restriction to $U$ of the action of an element of the finite-dimensional group of $1$-quasiconformal smooth mappings.

Keywords: mapping with bounded distortion, Carnot group, coercive estimate.

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English version:
Siberian Mathematical Journal, 2014, 55:5, 893–903

Bibliographic databases:

Document Type: Article
UDC: 517.54
Received: 20.12.2013

Citation: D. V. Isangulova, “The Liouville theorem for conformal mappings on Carnot groups with Goursat–Darboux distribution”, Sibirsk. Mat. Zh., 55:5 (2014), 1091–1103; Siberian Math. J., 55:5 (2014), 893–903

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\pages 1091--1103
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