Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds

  title={Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds},
  author={Juha M. Heinonen and Stephen Keith},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  • J. Heinonen, S. Keith
  • Published 17 September 2009
  • Mathematics
  • Publications mathématiques de l'IHÉS
We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in Rn. The condition is a Sobolev condition for a measurable coframe of flat 1-forms. In combination with an earlier work of D. Sullivan, our methods also yield an analytic characterization for smoothability of a Lipschitz manifold in terms of a Sobolev regularity for frames in a cotangent structure. In the proofs, we exploit the duality between flat chains and flat forms, and… 

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