Failure of Topological Rigidity Results for the Measure Contraction Property
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
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Potential AnalysisDate
2015Copyright
© 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.
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.
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Springer NetherlandsISSN Search the Publication Forum
0926-2601Keywords
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