An area formula for contact C 1-mappings of Carnot manifolds

DOI10.1080/17476930903510235zbMath1193.51015OpenAlexW2094549512MaRDI QIDQ3406627

M. B. Karmanova, Sergei Vodop'yanov

Publication date: 19 February 2010

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930903510235

zbMATH Keywords

area formulaCarnot manifoldsub-Riemannian

Mathematics Subject Classification ID

Metric geometry (51F99) General theory of differentiable manifolds (58A99) Local differential geometry (53B99)

Related Items (7)

Metric properties of classes of Hölder surfaces on Carnot groups ⋮ The tangent cone to a quasimetric space with dilations ⋮ Area formulas for classes of Hölder continuous mappings of Carnot groups ⋮ Measure of images of contact mappings on two-step sub-Lorentzian structures ⋮ An example of a Carnot manifold with \(C^{1}\)-smooth basis vector fields ⋮ Convergence of scaled vector fields and local approximation theorem on Carnot-Carathéodory spaces and applications ⋮ On the class of Hölder surfaces in Carnot-Carathéodory spaces

Cites Work

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• Balls and metrics defined by vector fields. I: Basic properties
• 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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