Consider the sub-Riemannian Heisenberg group . In this paper, we answer the following question: given a compact set and a continuous map , when is there a horizontal curve such that ? Whitney originally answered this question for real valued mappings, and Fefferman provided a complete answer for real valued functions defined on subsets of . We also prove a finiteness principle for horizontal curves in the Heisenberg group in the sense of Brudnyi and Shvartsman.
Cite this article
Scott Zimmerman, Whitney’s extension theorem and the finiteness principle for curves in the Heisenberg group. Rev. Mat. Iberoam. 39 (2023), no. 2, pp. 539–562DOI 10.4171/RMI/1339