On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target

@inproceedings{DeJarnette2011OnTL,
  title={On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target},
  author={Noel R. DeJarnette and Piotr Hajłasz and Anton Lukyanenko and Jeremy T. Tyson},
  year={2011}
}
  • Noel R. DeJarnette, Piotr Hajłasz, +1 author Jeremy T. Tyson
  • Published 2011
  • Mathematics
  • We study the question: when are Lipschitz mappings dense in the Sobolev space W (M, H)? Here M denotes a compact Riemannian manifold with or without boundary, while H denotes the nth Heisenberg group equipped with a sub-Riemannian metric. We show that Lipschitz maps are dense in W (M, H) for all 1 ≤ p < ∞ if dim M ≤ n, but that Lipschitz maps are not dense in W (M, H) if dim M ≥ n + 1 and n ≤ p < n + 1. The proofs rely on the construction of smooth horizontal embeddings of the sphere S into H… CONTINUE READING

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