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. doi:10.1007/s11118-014-9450-5
Published inPotential Analysis
© 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.