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

Noel DeJarnette, Piotr Hajlasz, Anton Lukyanenko +1

We study the question: when are Lipschitz mappings dense in the Sobolev space $W^{1,p}(M,{\mathbf{H}}^n)$? Here $M$ denotes a compact Riemannian manifold with or without boundary, wh…