A Compactness Theorem for Complete Ricci Shrinkers
By Robert Haslhofer, Reto Müller. 2010
101 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/cf641dc8755fbf493e7c9896ada1535aa607bfc8
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- Geometry of shrinking Ricci solitons (2014, result): “orbifold compactness result for four dimensional shrinking gradient Ricci solitons, improving various earlier results [5, 18, 29, 28].”
- Geometry of manifolds with densities (2012, background): “solitons, which satisfy the equation Ricf = 1 2, one has |∇f| 2 ≤ f. Also, if p is chosen to be a minimum point of f, then f (p) ≤ n 2 and the constant C0 in Theorem 2.2 depends only on n as shown in [13]. We now prove Theorem 1.1. For this, we will follow the argument in Lemma 2.1 of [23]. First, l”
- Analysis of weighted Laplacian and applications to Ricci solitons (2011, background): “According to [6, 12], d (p, x) − a ≤ ρ(x) ≤ d (p, x) + a, for a constant a > 0 depending only on n.”