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Failure of Topological Rigidity Results for the Measure Contraction Property

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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 \(\mathbb {R}\), 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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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Christian Ketterer

  2. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014, Jyväskylä, Finland

    Tapio Rajala

Authors
  1. Christian Ketterer
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  2. Tapio Rajala
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Correspondence to Tapio Rajala.

Additional information

T.R. acknowledges the support of the Academy of Finland projects number 137528 and 274372.

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Ketterer, C., Rajala, T. Failure of Topological Rigidity Results for the Measure Contraction Property. Potential Anal 42, 645–655 (2015). https://doi.org/10.1007/s11118-014-9450-5

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  • DOI: https://doi.org/10.1007/s11118-014-9450-5

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