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

@article{Heinonen2009FlatFB, 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}, year={2009}, volume={113}, pages={1-37} }

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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