On low-dimensional Ricci limit spaces

Shouhei Honda

doi:10.1215/00277630-1959442

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Home > Journals > Nagoya Math. J. > Volume 209 > Article

March 2013 On low-dimensional Ricci limit spaces

Shouhei Honda

Nagoya Math. J. 209: 1-22 (March 2013). DOI: 10.1215/00277630-1959442

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Abstract

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.