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- W2023286346 abstract "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." @default.
- W2023286346 created "2016-06-24" @default.
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- W2023286346 date "2011-04-05" @default.
- W2023286346 modified "2023-10-18" @default.
- W2023286346 title "Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds" @default.
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- W2023286346 doi "https://doi.org/10.1007/s10240-011-0032-4" @default.
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