Calculus of Variations and Geometric Measure Theory

R. Haslhofer - R. Buzano

A compactness theorem for complete Ricci shrinkers

created by muller on 12 Jun 2018
modified on 13 Jun 2022


Published Paper

Inserted: 12 jun 2018
Last Updated: 13 jun 2022

Journal: Geometric and Functional Analysis (GAFA)
Volume: 21
Year: 2011
Doi: 10.1007/s00039-011-0137-4

ArXiv: 1005.3255 PDF

Note name change of one author from Reto Müller to Reto Buzano in 2015. Please cite as Haslhofer-Müller. Name changed here in order to import to author page correctly.


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.