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On low-dimensional Ricci limit spaces

Published online by Cambridge University Press:  11 January 2016

Shouhei Honda
Shouhei Honda*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan, honda@kurims.kyoto-u.ac.jp
*
Faculty of Mathematics, Kyushu University, Fukuoka 819-0395, Japan, honda@math.kyushu-u.ac.jp
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Abstract

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We call a Gromov–Hausdorff limit of complete Riemannian manifolds with a lower bound of Ricci curvature a Ricci limit space. Furthermore, we prove that any Ricci limit space has integral Hausdorff dimension, provided that its Hausdorff dimension is not greater than 2. We also classify 1-dimensional Ricci limit spaces.

Keywords

53C2053C21
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 209 , March 2013 , pp. 1 - 22
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

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