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Juillet, Nicolas; Sigalotti, Mario

Pliability, or the Whitney extension theorem for curves in Carnot groups. (English) Zbl 1372.22009

Anal. PDE 10, No. 7, 1637-1661 (2017).
Simple arguments show that the Whitney extension theorem does not generalize to every ordered pair of Carnot groups. The authors consider the extendability problem for general ordered pairs \(({\mathbb R}, G)\), and characterize the nonabelian groups \(G\) for which the Whitney extension property holds, in terms of a newly introduced notion called pliability. They extend such results to all pliable Carnot groups, and show that the latter may be of arbitrarily large step.
Reviewer: George Stoica (Saint John)

Cited in 1 Review
Cited in 6 Documents

MSC:

22E25 Nilpotent and solvable Lie groups
41A05 Interpolation in approximation theory
53C17 Sub-Riemannian geometry
54C20 Extension of maps
58C25 Differentiable maps on manifolds

Keywords:

Whitney extension theorem; Carnot group; rigid curve; horizontal curve
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\textit{N. Juillet} and \textit{M. Sigalotti}, Anal. PDE 10, No. 7, 1637--1661 (2017; Zbl 1372.22009)
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