caa a22 4500 44584941X CHVBK 20180317145409.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s10240-011-0032-4 doi (NATIONALLICENCE)springer-10.1007/s10240-011-0032-4 Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds [Elektronische Daten] [Juha Heinonen, Stephen Keith] We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in R n . 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 recently established differential analysis on metric measure spaces. When specialized to R n , our result gives a kind of asymptotic and Lipschitz version of the measurable Riemann mapping theorem as suggested by Sullivan. IHES and Springer-Verlag, 2011 Heinonen Juha Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA aut Keith Stephen Sydney, Australia aut Publications mathématiques de l'IHÉS Springer-Verlag 113/1(2011-06-01), 1-37 0073-8301 113:1<1 2011 113 10240 https://doi.org/10.1007/s10240-011-0032-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10240-011-0032-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Heinonen Juha Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA aut NATIONALLICENCE 700 1- Keith Stephen Sydney, Australia aut NATIONALLICENCE 773 0- Publications mathématiques de l'IHÉS Springer-Verlag 113/1(2011-06-01), 1-37 0073-8301 113:1<1 2011 113 10240 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer