Differentiability and approximate differentiability for intrinsic Lipschitz functions in Carnot groups and a Rademacher theorem

DOI10.2478/agms-2014-0010zbMath1307.22007OpenAlexW2078954710MaRDI QIDQ483947

Bruno Franchi, Raul Paolo Serapioni, Marco Marchi

Publication date: 17 December 2014

Published in: Analysis and Geometry in Metric Spaces (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/agms-2014-0010

zbMATH Keywords

Carnot groupRademacher's theoremCarnot-Carathéodory distanceintrinsic differentiable functionintrinsic Lipschitz functionrectifiable set

Mathematics Subject Classification ID

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

Related Items (16)

On rectifiable measures in Carnot groups: Marstrand-Mattila rectifiability criterion ⋮ Intrinsic Lipschitz graphs within Carnot groups ⋮ On rectifiable measures in Carnot groups: existence of density ⋮ On rectifiable measures in Carnot groups: representation ⋮ Towards a theory of area in homogeneous groups ⋮ Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2 ⋮ Nowhere differentiable intrinsic Lipschitz graphs ⋮ Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces ⋮ Intrinsic Lipschitz graphs in Carnot groups of step 2 ⋮ Intrinsic Difference Quotients ⋮ Intrinsic differentiability and intrinsic regular surfaces in Carnot groups ⋮ Modules of systems of measures on polarizable Carnot groups ⋮ Characterizations of \(k\)-rectifiability in homogeneous groups ⋮ Intrinsic regular surfaces of low codimension in Heisenberg groups ⋮ Intrinsically Lipschitz functions with normal target in Carnot groups ⋮ Lipschitz graphs and currents in Heisenberg groups

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