Analytic properties of quasiconformal mappings on Carnot groups

DOI10.1007/BF02106836zbMath0891.30013OpenAlexW1972945275MaRDI QIDQ1920864

Sergei Vodop'yanov, Aleksandr Valer'evich Greshnov

Publication date: 30 June 1998

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02106836

zbMATH Keywords

Heisenberg groupsCarnot groupsACL-property

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Discrete subgroups of Lie groups (22E40) Global Riemannian geometry, including pinching (53C20)

Related Items (12)

Monotone functions and quasiconformal mappings on Carnot groups ⋮ Extremal length for quasiregular mappings on Heisenberg groups. ⋮ Sobolev mappings and moduli inequalities on Carnot groups ⋮ Mappings with bounded \((P,Q)\)-distortion on Carnot groups ⋮ The regularity of inverses to Sobolev mappings and the theory of \(\mathcal{Q}_{q,p} \)-homeomorphisms ⋮ A classification of sub-Riemannian manifolds ⋮ The Beltrami equations for quasiconformal mappings on strongly pseudoconvex hypersurfaces ⋮ \(p\)-module of vector measures in domains with intrinsic metric on Carnot groups ⋮ Integral representations and embedding theorems for functions defined on the Heisenberg groups $\mathbb H^n$ ⋮ Quasiconformal maps in metric spaces with controlled geometry ⋮ Sobolev spaces and \((P,Q)\)-quasiconformal mappings of Carnot groups ⋮ Sobolev classes of Banach space-valued functions and quasiconformal mappings

Cites Work

• Extremal length and functional completion
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• A remark on quasiconformal mappings on Carnot groups
• Foundations for the theory of quasiconformal mappings on the Heisenberg group
• Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)
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