Calculus of Variations and Geometric Measure Theory

N. Gigli - A. Mondino - T. Rajala

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


Accepted Paper

Inserted: 19 apr 2013
Last Updated: 15 jul 2013

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


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