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

• Scott Zimmerman ^[1]
  1. [1] Ohio State University at Marion

     Ohio State University at Marion

     Township of Marion, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 2, 2023, págs. 539-562
• Idioma: inglés
• DOI: 10.4171/RMI/1339
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• Resumen

  • 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.