Abstract
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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Haslhofer, R., Müller, R. A Compactness Theorem for Complete Ricci Shrinkers. Geom. Funct. Anal. 21, 1091–1116 (2011). https://doi.org/10.1007/s00039-011-0137-4
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DOI: https://doi.org/10.1007/s00039-011-0137-4