Pliability, or the Whitney extension theorem for curves in Carnot groups
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Publication:2402496
DOI10.2140/apde.2017.10.1637zbMath1372.22009arXiv1603.02639OpenAlexW3104312321MaRDI QIDQ2402496
Nicolas Juillet, Mario Sigalotti
Publication date: 7 September 2017
Published in: Analysis \& PDE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1603.02639
Nilpotent and solvable Lie groups (22E25) Interpolation in approximation theory (41A05) Extension of maps (54C20) Differentiable maps on manifolds (58C25) Sub-Riemannian geometry (53C17)
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On rectifiable measures in Carnot groups: Marstrand-Mattila rectifiability criterion ⋮ A rectifiability result for finite-perimeter sets in Carnot groups ⋮ Lusin approximation for horizontal curves in step 2 Carnot groups ⋮ A C^k Lusin approximation theorem for real-valued functions on Carnot groups ⋮ Whitney's extension theorem and the finiteness principle for curves in the Heisenberg group ⋮ A \(C^{m,\omega}\) Whitney extension theorem for horizontal curves in the Heisenberg group ⋮ A $C^m$ Whitney extension theorem for horizontal curves in the Heisenberg group ⋮ On the Whitney extension property for continuously differentiable horizontal curves in sub-Riemannian manifolds ⋮ A \(C^m\) Lusin approximation theorem for horizontal curves in the Heisenberg group
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