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Journal of the London Mathematical Society Advance Access originally published online on September 21, 2007
Journal of the London Mathematical Society 2007 76(1):225-236; doi:10.1112/jlms/jdm057
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© 2007 London Mathematical Society

Products, cones, and suspensions of spaces with the measure contraction property

Shin-Ichi Ohta

Department of Mathematics
Faculty of Science
Kyoto University
Kyoto 606-8502
Japan

This article concerns several geometric properties of metric measure spaces satisfying the measure contraction property (MCP), which can be considered as a generalized notion of lower Ricci curvature bounds. We prove that the MCP of spaces descends to their products and Euclidean cones. We also show that a positively curved space in terms of the MCP with a maximal diameter can be represented as the spherical suspension of some topological measure space.

sohta{at}math.kyoto-u.ac.jp

2000 Mathematics Subject Classification 28C15, 53C21, 53C23.

Received October 31, 2005; revised December 19, 2006; published online September 21, 2007.


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