Calculus of Variations and Geometric Measure Theory
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R. Haslhofer - R. Müller

A compactness theorem for complete Ricci shrinkers

created by muller on 19 May 2010
modified on 12 Jun 2018


Published Paper

Inserted: 19 may 2010
Last Updated: 12 jun 2018

Journal: Geom. Funct. Anal.
Volume: 21
Pages: 1091-1116
Year: 2011

ArXiv: 1005.3255 PDF


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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