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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


Ricci curvature and Lp-convergence

Shouhei Honda
Published Online: 2013-07-23 | DOI: https://doi.org/10.1515/crelle-2013-0061


We give the definition of Lp-convergence of tensor fields with respect to the Gromov–Hausdorff topology and several fundamental properties of the convergence. We apply this to establish a Bochner-type inequality which keeps the term of Hessian on the Gromov–Hausdorff limit space of a sequence of Riemannian manifolds with a lower Ricci curvature bound and to give a geometric explicit formula for the Dirichlet Laplacian on a limit space defined by Cheeger–Colding. We also prove the continuity of the first eigenvalues of the p-Laplacian with respect to the Gromov–Hausdorff topology.

About the article

Received: 2012-12-12

Revised: 2013-06-12

Published Online: 2013-07-23

Published in Print: 2015-08-01

Funding Source: Grant-in-Aid for Young Scientists (B)

Award identifier / Grant number: 24740046

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2015, Issue 705, Pages 85–154, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2013-0061.

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