An area formula for Lipschitz mappings of Carnot-Carathéodory spaces

DOI10.1070/IM2014v078n03ABEH002695zbMath1305.53042MaRDI QIDQ5495176

M. B. Karmanova

Publication date: 31 July 2014

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

zbMATH Keywords

differentiabilityJacobianarea formulaCarnot-Carathéodory spacesub-Riemannian manifoldLipschitz mappingsub-Riemannian quasi-metric

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Nilpotent and solvable Lie groups (22E25) Hausdorff and packing measures (28A78) Sub-Riemannian geometry (53C17)

Related Items (16)

Graph surfaces on five-dimensional sub-Lorentzian structures ⋮ Area formula for graph surfaces on five-dimensional sub-Lorentzian structures ⋮ Metric properties of classes of Hölder surfaces on Carnot groups ⋮ On local metric characteristics of level sets of \(C_H^1\)-mappings of Carnot manifolds ⋮ Local metric properties of level surfaces on Carnot-Carathéodory spaces ⋮ Area formulas for classes of Hölder continuous mappings of Carnot groups ⋮ Two-step sub-Lorentzian structures and graph surfaces ⋮ Measure of images of contact mappings on two-step sub-Lorentzian structures ⋮ The area of graphs on arbitrary Carnot groups with sub-Lorentzian structure ⋮ Unnamed Item ⋮ On the class of Hölder surfaces in Carnot-Carathéodory spaces ⋮ The area formula for graphs on 4-dimensional 2-step sub-Lorentzian structures ⋮ Properties of minimal surfaces over depth 2 Carnot manifolds ⋮ Area of graph surfaces on Carnot groups with sub-Lorentzian structure ⋮ Level sets of classes of mappings of two-step Carnot groups in a nonholonomic interpretation ⋮ Area formulas in metric measure spaces under a weak Lipschitz-like condition

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