Geometry and quasisymmetric parametrization of Semmes spaces
Pankka, P., & Wu, J.-M. (2014). Geometry and quasisymmetric parametrization of Semmes spaces. Revista matematica Iberoamericana, 30(3), 893-960. https://doi.org/10.4171/rmi/802
Published in
Revista matematica IberoamericanaDate
2014Copyright
© 2014 European Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by EMS. Published in this repository with the kind permission of the publisher.
We consider decomposition spaces R
3
/G that are manifold
factors and admit defining sequences consisting of cubes-with-handles
of finite type. Metrics on R
3
/G constructed via modular embeddings
of R
3
/G into a Euclidean space promote the controlled topology to a
controlled geometry.
The quasisymmetric parametrizability of the metric space R
3
/G×R
m
by R
3+m for any m ≥ 0 imposes quantitative topological constraints, in
terms of the circulation and the growth of the cubes-with-handles, on
the defining sequences for R
3
/G. We give a necessary condition and a
sufficient condition for the existence of such a parametrization.
The necessary condition answers negatively a question of Heinonen
and Semmes on quasisymmetric parametrizability of spaces associated
to the Bing double. The sufficient condition gives new examples of
quasispheres in S
4
.
Publisher
European Mathematical Society Publishing House; Real Sociedad Matematica EspanolaISSN Search the Publication Forum
0213-2230Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/24024378
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