A compactness theorem for complete Ricci shrinkers

Details A compactness theorem for complete Ricci shrinkers A compactness theorem for complete Ricci shrinkers

2010-05-18

arxiv.org/abs/1005.3255v3

Geom. Funct. Anal. (GAFA). 21 (2011), 1091--1116

Mathematics

Differential Geometry

28 pages, final version, to appear in GAFA

Scientific paper

10.1007/s00039-011-0137-4

We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds. In dimension four, under a technical assumption, we can replace the local integral Riemann bound by an upper bound for the Euler characteristic. The proof relies on a Gauss-Bonnet with cutoff argument.

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