Failure of Topological Rigidity Results for the Measure Contraction Property

Ketterer, Christian; Rajala, Tapio

doi:10.1007/s11118-014-9450-5

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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

Julkaistu sarjassa

Potential Analysis

Tekijät

Ketterer, Christian |

Rajala, Tapio

Päivämäärä

2015

Oppiaine

Matematiikka Mathematics

Tekijänoikeudet

© 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.

Julkaisija

Springer Netherlands

ISSN Hae Julkaisufoorumista

0926-2601