Mathematical Research Letters

Volume 17 (2010)

Number 6

Lipschitz extensions into Jet space Carnot groups

Pages: 1137 – 1149



Stefan Wenger (Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607–7045)

Robert Young (Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012)


The aim of this article is to prove a Lipschitz extension theorem for partially defined Lipschitz maps to jet spaces endowed with a left-invariant sub-Riemannian Carnot-Carathéodory distance. The jet spaces give a model for a certain class of Carnot groups, including in particular all Heisenberg groups. The proofs or our theorems are rather elementary, they are inspired by ideas in papers of Gromov, Young, and Lang-Schlichenmaier.

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