Analysis and Geometry on Singular Spaces

Examples of branching metric spaces with Ricci curvature lower bounds

Tapio Rajala (University of Jyväskylä)

created by paolini on 25 Apr 2014
modified by gigli on 08 May 2014

Abstract.

I will discuss the role of the non-branching assumption in different notions of Ricci curvature lower bounds in metric measure spaces. I will briefly recall results on CD(K,N) and MCP(K,N) spaces that were proven originally under the non-branching assumption. After this we will see how the simple example of a branching space satisfying CD(0,2), namely the plane with the supremum norm, can be modified to give counter-examples to some of these results in the branching case. We will obtain a counter-example to the local-to-global property on CD(K,N) spaces and counter-examples to topological splitting and maximal diameter theorems in MCP(K,N) spaces. This last set of examples were observed together with Christian Ketterer.

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