Theoretical analysis compares non-rigidity notions of horizontal vectors in Carnot groups, highlighting relationships relevant to monotone sets and Whitney extensions.
In recent years, several notions of non-rigidity of horizontal vectors in Carnot groups have been proposed, motivated, in particular, by the characterization of monotone sets and Whitney extension properties. In this note we compare some of these notions.
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Jean et al. (2026) studied this question.
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