Resumen de Whitney’s extension theorem and the finiteness principle for curves in the Heisenberg group

Scott Zimmerman

• Consider the sub-Riemannian Heisenberg group H. In this paper, we answer the following question: given a compact set K⊆R and a continuous map f:K→H, when is there a horizontal Cm curve F:R→H such that F∣K=f? Whitney originally answered this question for real valued mappings, and Fefferman provided a complete answer for real valued functions defined on subsets of Rn. We also prove a finiteness principle for Cm,ω horizontal curves in the Heisenberg group in the sense of Brudnyi and Shvartsman.