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.

A Compactness Theorem for Complete Ricci Shrinkers

Müller, Reto
2011

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.
21
5
1091
1116
https://arxiv.org/abs/1005.3255
Gauss-Bonnet with boundary; Ricci flow; Ricci solitons; Analysis; Geometry and Topology
Haslhofer, Robert; Müller, Reto
File in questo prodotto:
File Dimensione Formato  
1005.3255.pdf

Accesso aperto con embargo fino al 01/10/2012

Tipo di file: POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione 308.18 kB
Formato Adobe PDF
308.18 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1701042
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 42
  • ???jsp.display-item.citation.isi??? 42
social impact