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

  • Nicola Gigli EMAIL logo , Andrea Mondino and Tapio Rajala
Published/Copyright: September 5, 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.

Funding source: ETH fellowship

Funding source: ERC

Award Identifier / Grant number: GeMeTheNES

Funding source: Academy of Finland

Award Identifier / Grant number: 137528

The second author acknowledges the support of the ETH fellowship, part of the work was written when he was supported by the ERC grant GeMeTheNES directed by Prof. Luigi Ambrosio. The third author acknowledges the support of the Academy of Finland project no. 137528.

Received: 2013-4-19
Revised: 2013-5-9
Published Online: 2013-9-5
Published in Print: 2015-8-1

© 2015 by De Gruyter

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