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.
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric mea- sure spaces with Ricci curvature bounded below / Gigli, Nicola; Mondino, Andrea; Rajala, T.. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 705:(2015), pp. 233-244. [10.1515/crelle-2013-0052]
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric mea- sure spaces with Ricci curvature bounded below
Gigli, Nicola;Mondino, Andrea;
2015-01-01
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.| File | Dimensione | Formato | |
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RCDtangents4.pdf
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