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Lipschitz non-extension theorems into jet space Carnot groups. (English) Zbl 1203.53028

It is interesting to consider Lipschitz extension theorems for Lipschitz maps. This paper studies Lipschitz maps with target spaces being jet spaces equipped with a left invariant Riemannian distances, as well as jet spaces equipped with a left invariant sub-Riemannian Carnot Carathéodory distance. This jet space gives a model for a certain class of C-C groups. The authours derive that there is not any extension results for Lipschitz maps with respect to this jet space.

MSC:

53C17 Sub-Riemannian geometry
58A30 Vector distributions (subbundles of the tangent bundles)
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