A compactness theorem for complete Ricci shrinkers
Differential Geometry
2011-11-04 v3
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.
Cite
@article{arxiv.1005.3255,
title = {A compactness theorem for complete Ricci shrinkers},
author = {Robert Haslhofer and Reto Müller},
journal= {arXiv preprint arXiv:1005.3255},
year = {2011}
}
Comments
28 pages, final version, to appear in GAFA