Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds |
| |
Authors: | Juha Heinonen and Stephen Keith |
| |
Institution: | (1) Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, Gustaf H?llstr?min katu 2b, 00014 Helsinki, Finland;(2) Departement Mathematik, ETH Z?rich, 8092 Zurich, Switzerland |
| |
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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|