# Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below

created by mondino on 19 Apr 2013
modified by rajala1 on 15 Jul 2013

[BibTeX]

Accepted Paper

Inserted: 19 apr 2013
Last Updated: 15 jul 2013

Journal: J. Reine Angew. Math.
Year: 2013

Abstract:

We show that in any infinitesimally Hilbertian $CD^*(K,N)$-space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space that converges to a Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian $CD^*(0,N)$-spaces.

Tags: GeMeThNES