Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

F. Cavalletti - K. T. Sturm

Local CD(K,N) implies MCP(K,N)

created by cavallett on 23 Feb 2012


Accepted Paper

Inserted: 23 feb 2012
Last Updated: 23 feb 2012

Journal: J. Funct. Anal.
Year: 2012


We prove that for non-branching metric measure spaces the local curvature condition CDloc(K,N) implies the global version of MCP(K,N). The curvature condition CD(K,N) introduced by the second author and also studied by Lott & Villani is the generalization to metric measure space of lower bounds on Ricci curvature together with upper bounds on the dimension. It is worth pointing out that our result implies sharp Bishop-Gromov volume growth inequality and sharp Poincar ́e inequality.


Credits | Cookie policy | HTML 5 | CSS 2.1