A Compactness Theorem for Complete Ricci Shrinkers |
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Authors: | Robert Haslhofer Reto M��ller |
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Institution: | 1. ETH Z??rich, R?mistrasse 101, 8092, Z??rich, Switzerland 2. Scuola Normale Superiore di Pisa, Piazza Cavelieri 7, 56126, Pisa, Italy
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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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