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arXiv · 1304.5359

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

Nicola Gigli·Andrea Mondino·Tapio Rajala
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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.

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Nicola Gigli, Andrea Mondino, Tapio Rajala. 2013-04-19. Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below. https://doi.org/10.1515/crelle-2013-0052

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