Failure of Topological Rigidity Results for the Measure Contraction Property
Abstract
We give two examples of metric measure spaces satisfying the measure contraction
property MCP(K, N) but having different topological dimensions at different
regions of the space. The first one satisfies MCP(0, 3) and contains a subset isometric to
R, but does not topologically split. The second space satisfies MCP(2, 3) and has diameter
π, which is the maximal possible diameter for a space satisfying MCP(N − 1, N), but is
not a topological spherical suspension. The latter example gives an answer to a question
by Ohta.
Main Authors
Format
Articles
Research article
Published
2015
Series
Subjects
Publication in research information system
Publisher
Springer Netherlands
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201508182693Use this for linking
Review status
Peer reviewed
ISSN
0926-2601
DOI
https://doi.org/10.1007/s11118-014-9450-5
Language
English
Published in
Potential Analysis
Citation
- Ketterer, C., & Rajala, T. (2015). Failure of Topological Rigidity Results for the Measure Contraction Property. Potential Analysis, 42(3), 645-655. https://doi.org/10.1007/s11118-014-9450-5
License
Copyright© Springer Science+Business Media Dordrecht 2014. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.