Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces

Details Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces

2010-03-10

arxiv.org/abs/1003.2116v1

Mathematics

Differential Geometry

25 pages, no figures

Scientific paper

This paper is devoted to the analysis of metric measure spaces satisfying locally the curvature-dimension condition CD(K,N) introduced by the second author and also studied by Lott & Villani. We prove that the local version of CD(K,N) is equivalent to a global condition CD*(K,N), slightly weaker than the (usual, global) curvature-dimension condition. This so-called reduced curvature-dimension condition CD*(K,N) has the local-to-global property. We also prove the tensorization property for CD*(K,N). As an application we conclude that the fundamental group of a metric measure space (M,d,m) is finite whenever it satisfies locally the curvature-dimension condition CD(K,N) with positive K and finite N.

Affiliated with

Also associated with

No associations

Rating

Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-342101