An area formula for \(C^{1}\)-smooth contact mappings of Carnot manifolds

DOI10.1134/S1064562408050037zbMath1180.53035MaRDI QIDQ1048485

M. B. Karmanova, Sergei Vodop'yanov

Publication date: 12 January 2010

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

tomographyroboticsneurobiologyCarnot groupssub-Riemannian measures

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Sub-Riemannian geometry (53C17) Differential geometric aspects of gerbes and differential characters (53C08)

Related Items (7)

A local approximation theorem on Carnot manifolds under minimal smoothness conditions ⋮ The tangent cone to a quasimetric space with dilations ⋮ Convergence of scaled vector fields and local approximation theorem on Carnot-Carathéodory spaces and applications ⋮ An area formula for Lipschitz mappings of Carnot-Carathéodory spaces ⋮ Characteristic sets for smooth contact mappings of Carnot-Carathéodory spaces ⋮ Tangent cone to a regular quasimetric Carnot-Carathéodory space ⋮ Algebraic properties of the tangent cone to a quasimetric space with dilations

Cites Work

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• A coarea formula for smooth contact mappings of Carnot manifolds
• Rectifiable sets in metric and Banach spaces
• Sobolev-type classes of functions with values in a metric space
• Local geometry of Carnot manifolds under minimal smoothness
• A notion of rectifiability modeled on Carnot groups

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