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

Abstract

We show that in any infinitesimally Hilbertian $C{D}^{\ast }(K,N)$-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 $C{D}^{\ast }(0,N)$-spaces.

13 pages

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