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A Compactness Theorem for Complete Ricci Shrinkers

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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Correspondence to Robert Haslhofer.

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

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Keywords and phrases

  • Ricci solitons
  • Ricci flow
  • Gauss–Bonnet with boundary

2010 Mathematics Subject Classification

  • 53C21
  • 53C23
  • 53C25
  • 53C44