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Products, cones, and suspensions of spaces with the measure contraction property
Author(s) -
Ohta Shin-Ichi
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm057
Subject(s) - measure (data warehouse) , contraction (grammar) , mathematics , metric space , ricci curvature , pure mathematics , euclidean space , mathematical analysis , property (philosophy) , suspension (topology) , euclidean geometry , curvature , space (punctuation) , topology (electrical circuits) , geometry , combinatorics , computer science , homotopy , medicine , philosophy , epistemology , database , operating system
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.