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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2015, Issue 705


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

Nicola Gigli / Andrea Mondino / Tapio Rajala
Published Online: 2013-09-05 | DOI: https://doi.org/10.1515/crelle-2013-0052


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.

About the article

Received: 2013-04-19

Revised: 2013-05-09

Published Online: 2013-09-05

Published in Print: 2015-08-01

Funding Source: ETH fellowship

Funding Source: ERC

Award identifier / Grant number: GeMeTheNES

Funding Source: Academy of Finland

Award identifier / Grant number: 137528

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2015, Issue 705, Pages 233–244, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2013-0052.

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